Notes 7-2
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![Page 1: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/1.jpg)
Section 7-2Addition Counting Principles
![Page 2: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/2.jpg)
Warm-upHow many positive integers less than or equal to 1000
satisfy each condition?
a. Divisible by 5? b. Divisible by 7?
Divisible by 5 or 7?
![Page 3: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/3.jpg)
Warm-upHow many positive integers less than or equal to 1000
satisfy each condition?
a. Divisible by 5? b. Divisible by 7?
Divisible by 5 or 7?
200
![Page 4: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/4.jpg)
Warm-upHow many positive integers less than or equal to 1000
satisfy each condition?
a. Divisible by 5? b. Divisible by 7?
Divisible by 5 or 7?
200 142
![Page 5: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/5.jpg)
Warm-upHow many positive integers less than or equal to 1000
satisfy each condition?
a. Divisible by 5? b. Divisible by 7?
Divisible by 5 or 7?
200 142
314
![Page 6: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/6.jpg)
Union:
![Page 7: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/7.jpg)
Union: Values that are in one set or another; does not need to be part of both
![Page 8: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/8.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
![Page 9: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/9.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
Disjoint/Mutually Exclusive:
![Page 10: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/10.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
Disjoint/Mutually Exclusive: A situation where two or more sets have nothing in common
![Page 11: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/11.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
Disjoint/Mutually Exclusive: A situation where two or more sets have nothing in common
i.e. Rolling a sum of 2 or 3 on a pair of dice; you can’t have them both happen at the same time
![Page 12: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/12.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
Disjoint/Mutually Exclusive: A situation where two or more sets have nothing in common
i.e. Rolling a sum of 2 or 3 on a pair of dice; you can’t have them both happen at the same time
Intersection:
![Page 13: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/13.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
Disjoint/Mutually Exclusive: A situation where two or more sets have nothing in common
i.e. Rolling a sum of 2 or 3 on a pair of dice; you can’t have them both happen at the same time
Intersection: Values that are shared by two or more sets
![Page 14: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/14.jpg)
Union: Values that are in one set or another; does not need to be part of both
Notation: A B
Disjoint/Mutually Exclusive: A situation where two or more sets have nothing in common
i.e. Rolling a sum of 2 or 3 on a pair of dice; you can’t have them both happen at the same time
Intersection: Values that are shared by two or more sets
Notation: A B
![Page 15: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/15.jpg)
Addition Counting Principle (Mutually Exclusive Form):
![Page 16: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/16.jpg)
Addition Counting Principle (Mutually Exclusive Form):
If two finite sets A and B are mutually exclusive, then
N(A B) = N(A)+ N(B)
![Page 17: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/17.jpg)
Addition Counting Principle (Mutually Exclusive Form):
If two finite sets A and B are mutually exclusive, then
N(A B) = N(A)+ N(B)
Theorem (Probability of the Union of Mutually Exclusive Events):
![Page 18: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/18.jpg)
Addition Counting Principle (Mutually Exclusive Form):
If two finite sets A and B are mutually exclusive, then
N(A B) = N(A)+ N(B)
Theorem (Probability of the Union of Mutually Exclusive Events):
If A and B are mutually exclusive events in the same finite sample space, then
P(A B) = P(A)+ P(B)
![Page 19: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/19.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
![Page 20: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/20.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
![Page 21: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/21.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
![Page 22: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/22.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
![Page 23: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/23.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
![Page 24: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/24.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
![Page 25: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/25.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
= 1
36+ 2
36
![Page 26: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/26.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
= 1
36+ 2
36 = 3
36
![Page 27: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/27.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
= 1
36+ 2
36 = 3
36 = 1
12
![Page 28: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/28.jpg)
Example 1a. If two fair dice are tossed, what is the probability that
the sum is 2 or 3?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum of 2 or 3)
= P(sum of2)+ P(sum of 3)
= 1
36+ 2
36 = 3
36 = 1
12
There is an 8 1/3 % chance of rolling a sum of 2 or 3
![Page 29: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/29.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
![Page 30: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/30.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
![Page 31: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/31.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum is even or > 4)
![Page 32: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/32.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 33: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/33.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 34: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/34.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 35: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/35.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
= 18
36
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 36: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/36.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
= 18
36 + 30
36
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 37: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/37.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
= 18
36 + 30
36 − 14
36
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 38: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/38.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
= 18
36 + 30
36 − 14
36 = 34
36
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 39: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/39.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
= 18
36 + 30
36 − 14
36 = 34
36 = 17
18
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 40: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/40.jpg)
Example 1b. If two dice are tossed, what is the probability that the
sum will be even or greater than 4?
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
= 18
36 + 30
36 − 14
36 = 34
36 = 17
18
There is a 94 4/9 % chance of rolling an even sum or a sum
greater than 4
P(sum is even or > 4)
= P(sum is even) + P(sum > 4)
![Page 41: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/41.jpg)
Addition Counting Principle (General Form):
![Page 42: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/42.jpg)
Addition Counting Principle (General Form):
For any finite sets A and B,
N(A B) = N(A)+ N(B)− N(A B)
![Page 43: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/43.jpg)
Addition Counting Principle (General Form):
Theorem (Probability of a Union of Events General Form):
For any finite sets A and B,
N(A B) = N(A)+ N(B)− N(A B)
![Page 44: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/44.jpg)
Addition Counting Principle (General Form):
Theorem (Probability of a Union of Events General Form):
For any finite sets A and B,
N(A B) = N(A)+ N(B)− N(A B)
If A and B are any events in the same finite sample space, then
P(A or B) = P(A B) = P(A)+ P(B)− P(A B)
![Page 45: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/45.jpg)
Example 2Thirteen of the 50 states include territory that lies west of the continental divide. Forty-two states include territory that lies east of the continental divide. Is this possible?
Explain.
![Page 46: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/46.jpg)
Example 2Thirteen of the 50 states include territory that lies west of the continental divide. Forty-two states include territory that lies east of the continental divide. Is this possible?
Explain.
Of course this is possible! This just means that some states have the continental divide running right though them!
![Page 47: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/47.jpg)
Example 2Thirteen of the 50 states include territory that lies west of the continental divide. Forty-two states include territory that lies east of the continental divide. Is this possible?
Explain.
Of course this is possible! This just means that some states have the continental divide running right though them!
Bonus: Which states would these be? The FIRST person to post the correct answer AFTER 7 PM on the wiki
under section 7-2 will earn some bonus points!
![Page 48: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/48.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
![Page 49: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/49.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
HHHHHTHTHTHH
HTTTHTTTHTTT
![Page 50: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/50.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
HHHHHTHTHTHH
HTTTHTTTHTTT
![Page 51: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/51.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
HHHHHTHTHTHH
HTTTHTTTHTTT
P(Not all 3 same)
![Page 52: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/52.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
HHHHHTHTHTHH
HTTTHTTTHTTT
P(Not all 3 same)
= 6
8
![Page 53: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/53.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
HHHHHTHTHTHH
HTTTHTTTHTTT
P(Not all 3 same)
= 6
8 = 3
4
![Page 54: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/54.jpg)
Example 3Three fair coins are tossed. What is the probability that not
all of the coins show the same face?
HHHHHTHTHTHH
HTTTHTTTHTTT
P(Not all 3 same)
= 6
8 = 3
4
There is a 75% chance of
getting not all 3 coins the same
![Page 55: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/55.jpg)
Complementary Events
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Complementary Events
When you have events whose union takes up the entire sample space, but the events are mutually exclusive
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Complementary Events
When you have events whose union takes up the entire sample space, but the events are mutually exclusive
The complement of R is not R
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Example 4Two dice are tossed. Find the probability that their sum is
not 6.
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Example 4Two dice are tossed. Find the probability that their sum is
not 6.
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
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Example 4Two dice are tossed. Find the probability that their sum is
not 6.
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
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Example 4Two dice are tossed. Find the probability that their sum is
not 6.
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(not 6)
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Example 4Two dice are tossed. Find the probability that their sum is
not 6.
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(not 6) = 31
36
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Example 4Two dice are tossed. Find the probability that their sum is
not 6.
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(not 6) = 31
36
There is an 86 1/9 % chance that the sum
will not be 6
![Page 64: Notes 7-2](https://reader034.fdocuments.in/reader034/viewer/2022051313/5482f3ebb47959140d8b48dc/html5/thumbnails/64.jpg)
Example 4Two dice are tossed. Find the probability that their sum is
not 6.
1,3 1,41,1 1,51,2 1,62,3 2,42,1 2,52,2 2,63,3 3,43,1 3,53,2 3,64,3 4,44,1 4,54,2 4,65,3 5,45,1 5,55,2 5,66,3 6,46,1 6,56,2 6,6
P(not 6) = 31
36
There is an 86 1/9 % chance that the sum
will not be 6
1− P(6) =1− 5
36= 31
36
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Theorem (Probability of Complements)
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Theorem (Probability of Complements)
In any event E, the complement of E is
P(not E) =1− P(E)
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Homework
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Homework
p. 437 #1-24