79 - Independent and Dependent Events...Independent & Dependent Events. Puzzle # 79 How do...
Transcript of 79 - Independent and Dependent Events...Independent & Dependent Events. Puzzle # 79 How do...
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Do Now
In a phys ed class at LaGuardia, 13 students out of 50 have a cat as a pet.
If there are 2,813 students attending the school,
to the nearest 10, how many of them have cats as pets?
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Do Now
In a phys ed class at LaGuardia, 13 students out of 50 have a cat as a pet.
If there are 2,813 students attending the school,
to the nearest 10, how many of them have cats as pets?
730
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Do Now
In a phys ed class at LaGuardia, 13 students out of 50 have a cat as a pet.
If there are 2,813 students attending the school,
to the nearest 10, how many of them have cats as pets?
1350
= 0.26
(2813)(0.26) = 731 which rounds to 730
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Puzzle # Title Page #
75 Modeling with Trig Functions
76 Trigonometric Identies
77 Probability
78 Empirical Probability
79 Independent & Dependent Events
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Puzzle # 79
How do independent and dependent events compare with each other?
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You toss a coin and roll a 4-sided die.
What is the probability you’ll get heads and a 3?
Think - 30 seconds
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You toss a coin and roll a 4-sided die.
Explain to one member of your group what the probability is
that you’ll get heads and a 3?
Pair - 20 seconds
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You toss a coin and roll a 4-sided die.
Share with your group what the probability is
that you’ll get heads and a 3?
Share - 20 seconds
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How does the toss of the coin affect the die?
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When the result of one activity has no influence
on the result of subsequent activities, they are independent events.
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Flipping a coin has two possible outcomes: heads or tails
Rolling a 4-sided die has four possible outcomes: 1, 2, 3, or 4
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H
T
1
2
3
41
2
3
4
Tree Diagram
H1 H2 H3 H4 T1 T2 T3 T4
P(H3) =18
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If there are a lot of possible outcomes making a tree diagram
can be very time consuming.
Fortunately, there’s a faster way to figure it out.
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P(A and B) = P(A) • P(B)
When two events are independent the product of both events happening
is the product of the probability of each event.
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If the product of two events happening is their product,
the events are independent.
Let’s look at the problem from the Think-Pair-Share
P(H3) =18
P(H) =12
P(3) =14
Since P(H3) = P(H) • P(3), the events are independent
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At Seaside Seafood, their salmon delivery comes 90% of the time,
40% of the customers order salmon, and there’s a 45% probability
that the salmon will be delivered and a customers will order it.
P(both) ≠ P(delivery) • P(order)
.45 ≠ .9 • .4
Therefore, the two events are not independent.
(Customers only order salmon if it’s been delivered.)
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There are 10 marbles in a box; four red, three blue, two green,
and one yellow.
What’s the probability of picking two red and one blue?
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What’s the probability of the first marble you pick
being red?
What’s the probability of the second marble you pick
being red?
410
39
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What’s the probability of the third marble you pick
being blue?
38
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P(RRG) = ( 410 ) ( 3
9 ) ( 38 ) =
36720
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When the result of one activity influences the results of subsequent activities,
those are dependent events.
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Determine the probability of all three marbles
being the same color.
P(3Red) = ( 410 ) ( 3
9 ) ( 28 ) =
24720
P(3Blue) = ( 310 ) ( 2
9 ) ( 18 ) =
6720
P(3Green) = 0, since there are fewer than 3 green marbles.
P(3Yellow) = 0, since there are fewer than 3 yellow marbles.
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Determine the probability of all three marbles
being the same color.
P(3Red) = ( 410 ) ( 3
9 ) ( 28 ) =
24720
P(3Blue) = ( 310 ) ( 2
9 ) ( 18 ) =
6720
P(3All) =24720
+6
720=
30720
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Exit Card # 79On a given school day,
the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps
and has a pop quiz on the same day?
06_18_11
1) 73%
2) 36%
3) 23%
4) 12%
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Exit Card # 79On a given school day,
the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps
and has a pop quiz on the same day?
06_18_11
1) 73%
2) 36%
3) 23%
4) 12%
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Exit Card # 79On a given school day,
the probability that Nick oversleeps is 48% and the probability he has a pop quiz is 25%. Assuming these two events are independent, what is the probability that Nick oversleeps
and has a pop quiz on the same day?
1) 73%
2) 36%
3) 23%
4) 12%
Since the two events are independent, 0.25 • 0.48 = 0.12