AP StatisticsAP Statistics

ProbabilityProbability

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Problem 1Problem 1A box contains six red tags numbered 1 through 6, and four white tags numbered 1 through 4.

One tag is drawn at random. Write the sample space for this experiment. Write the sample space for this experiment.

S = {R1, R2, R3, R4, R5, R6, W1, S = {R1, R2, R3, R4, R5, R6, W1, W2, W3, W4}W2, W3, W4}

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Problem 2 - 5Problem 2 - 5A box contains six red tags numbered 1 through 6, and four white tags numbered 1 through 4.

One tag is drawn at random.

Calculate the following probabilities:Calculate the following probabilities:

2.2. P(red) =P(red) =

3. P(even number) =

4. P(red and even) =

5. P(red or even) =

.65

3

10

6

.52

1

10

5

.310

3

.85

4

10

8

4

Problem 6 - 9Problem 6 - 9A box contains six red tags numbered 1 through 6, and four white tags numbered 1 through 4.

One tag is drawn at random.

Calculate the following probabilities:Calculate the following probabilities:

6.6. P(neither red nor even) =P(neither red nor even) =

7. P(even|red) =

8. P(red|even) =

9. P(<4 |odd) =

.25

1

10

2

.52

1

6

3

.65

3

.85

4

5

Question 10Question 10 Suppose that for a group of consumers, the

probability of eating pretzels is .75 and that the probability of drinking Coke is .65. Further suppose that the probability of eating pretzels and drinking Coke is .55. Determine if these two events are independent.

If they are independent, then:If they are independent, then:P(eating a pretzel and drinking a coke)P(eating a pretzel and drinking a coke)=P(eating a pretzel) x P(drinking a coke) =P(eating a pretzel) x P(drinking a coke) However, (.75)(.65) = 0.4875 ≠ 0.55. However, (.75)(.65) = 0.4875 ≠ 0.55. Therefore the events are NOT Therefore the events are NOT independent.independent.

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Problem 11 - 14Problem 11 - 14Given that the probability of A is ½, the probability for B is 3/5, and the probability of both A and B is

1/5.

Answer the following:Answer the following:

11.11. Are the events disjoint?Are the events disjoint?

12.Are the events independent?

13.P(A ∩ BC) =

14.P(AC ∩ B) =

!!!NO

!!!NO

.310

3

.410

4

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Problem 15 - 18Problem 15 - 18Given that the probability of A is ½, the probability for B is 3/5, and the probability of both

A and B is 1/5.

Answer the following:Answer the following:

15.15. P(AC ∩ BC) =

16.P(B|A) =

17.P(BC|A) =

18.P(BC|AC) =

.110

1

.45

2

.65

3

.110

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