13.1 Theoretical Probability
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ProbabilityProbability
Student Study Guide13.1 Theoretical Probability
Student Study Guide13.1 Theoretical Probability
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A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is
1. 14
A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is
1. 14
1501
50
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A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is2. Less than 37
A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is2. Less than 37
36 numbers less than 3736 numbers less than 37
36 5036 50
= 18 25= 18 25
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A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is
3. A perfect square
A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is
3. A perfect square1x1=1, 2x2=4, 3x3=9, 4x4=16, 5x5=25, 6x6=36,
7x7=49, 8x8=64
1x1=1, 2x2=4, 3x3=9, 4x4=16, 5x5=25, 6x6=36,
7x7=49, 8x8=647 507 50
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A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is
4. Odd and less than 25
A chip is drawn at random from a bag of chips numbered from 1 to 50 inclusive. Find
the probability that the number drawn is
4. Odd and less than 251, 3, 5, 7, 9, 11, 13, 15, 17, 19,
21, 231, 3, 5, 7, 9, 11, 13, 15, 17, 19,
21, 2312 5012 50
= 6 25= 6 25
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A coin is tossed 3 times. Find each probability.
5. P(3 heads)
A coin is tossed 3 times. Find each probability.
5. P(3 heads)
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
1 81 8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
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A coin is tossed 3 times. Find each probability.
6. P(exactly 1 tails)
A coin is tossed 3 times. Find each probability.
6. P(exactly 1 tails)
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
3 83 8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
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A coin is tossed 3 times. Find each probability.
7. P(at least 1 heads)
A coin is tossed 3 times. Find each probability.
7. P(at least 1 heads)
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
7 87 8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
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A coin is tossed 3 times. Find each probability.
7. P(at least 1 heads)
A coin is tossed 3 times. Find each probability.
7. P(at least 1 heads)
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
7 87 8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
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A coin is tossed 3 times. Find each probability.
8. P(at least 2 heads)
A coin is tossed 3 times. Find each probability.
8. P(at least 2 heads)
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
4 84 8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
= 1 2= 1 2
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Practice Masters Level BPractice Masters Level B
13.1 Theoretical Probability13.1 Theoretical Probability
#2 - Sample Space#2 - Sample Space
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2. Rolling a number cube and then tossing a coin
2. Rolling a number cube and then tossing a coin
1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T
1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T
2 x 6 = 122 x 6 = 12
2 sides on a coin6 sides on a cube2 sides on a coin6 sides on a cube
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Find the number of favorable outcomes in the sample space
for each experiment. 4. A number cube is rolled
twice. The sum of the rolls is 6.
Find the number of favorable outcomes in the sample space
for each experiment. 4. A number cube is rolled
twice. The sum of the rolls is 6.
1+5, 5+1, 2+4, 4+2, 3+31+5, 5+1, 2+4, 4+2, 3+3
55
5 different options5 different options
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Suppose that you select a letter of the English alphabet at random.
Find the probability of each event.7. The letter is in the word
Mississipi.
Suppose that you select a letter of the English alphabet at random.
Find the probability of each event.7. The letter is in the word
Mississipi.26 letters in the alphabet26 letters in the alphabet
4264
26
4 different letters4 different letters
m, i, s, pm, i, s, p
= 2 13= 2 13
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Suppose that you select a letter of the English alphabet at random.
Find the probability of each event.8. The letter is in the word Ohio.
Suppose that you select a letter of the English alphabet at random.
Find the probability of each event.8. The letter is in the word Ohio.
26 letters in the alphabet26 letters in the alphabet
3263
26
3 different letters3 different letters
O, h, iO, h, i
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Find the probability of each outcome.
14. Two rolls of a number cube will have a sum of 7.
Find the probability of each outcome.
14. Two rolls of a number cube will have a sum of 7.
1+6, 6+1, 3+4, 4+3, 2+5, 5+21+6, 6+1, 3+4, 4+3, 2+5, 5+2
6?6?
6 different combinations6 different combinations
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14. Two rolls of a number cube will have a sum of 7.
14. Two rolls of a number cube will have a sum of 7.
36 possibilities
6x6=36
36 possibilities
6x6=36
1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,
6+6
1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,
6+6 636
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Find the probability of each outcome.
15. Two tosses of a coin will be two heads.
Find the probability of each outcome.
15. Two tosses of a coin will be two heads.
14
HH, HT, TH, TTHH, HT, TH, TTHH, HT, TH, TTHH, HT, TH, TT
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Find the probability of each outcome.
16. Two rolls of a number cube will have an odd sum.
Find the probability of each outcome.
16. Two rolls of a number cube will have an odd sum.
18 ?
Odd + Even number = Odd Sum
Odd + Even number = Odd Sum
1+2, 1+4, 1+6, 2+1, 2+3, 2+5, 3+2, 3+4, 3+6, 4+1, 4+3, 4+5, 5+2, 5+4, 5+6, 6+1, 6+3, 6+5
1+2, 1+4, 1+6, 2+1, 2+3, 2+5, 3+2, 3+4, 3+6, 4+1, 4+3, 4+5, 5+2, 5+4, 5+6, 6+1, 6+3, 6+5
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16. Two rolls of a number cube will have an odd sum.
16. Two rolls of a number cube will have an odd sum.
36 possible outcomes
1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,
6+6
1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 2+1, 2+2, 2+3, 2+4, 2+5, 2+6, 3+1, 3+2, 3+3, 3+4, 3+5, 3+6, 4+1, 4+2, 4+3, 4+4, 4+5, 4+6, 5+1, 5+2, 5+3, 5+4, 5+5, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5,
6+6 1836