1

Let A and B be two independent events. If P(A) = 0.5, what can you say about P(A | B)?

1. Cannot find it because P(B) is not known.
2. Cannot find it because P(A and B) is not known.
3. Cannot find it because both P(B) and P(A and B) are not known.
4. It is equal to 0.5.
5. It is equal to 0.25.

Question 2

Suppose a basketball team had a season of games with the following characteristics:

• Of all the games, 60% wereat-homegames. Denote this byH(the remaining wereawaygames).
• Of all the games, 25% werewins. Denote this byW(the remaining werelosses).
• Of all the games, 20% were at-home wins.

Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)

1. 0.12
2. 0.15
3. 0.20
4. 0.33
5. 0.42

Question 3

Suppose your friends have the following ice cream flavor preferences:

• 70% of your friends like chocolate (C). The remaining do not like chocolate.
• 40% of your friends sprinkles (S) topping. The remaining do not like sprinkles.
• 25% of your friends like chocolate (C) and also like sprinkles (S).

If your friend had chocolate, how likely is it that they also had sprinkles? (Note: Some answers are rounded to 2 decimal places).

1. 0.10
2. 0.18
3. 0.28
4. 0.36
5. 0.63

Question 4

Suppose that the handedness of the last fifteen U.S. presidents is as follows:

• 40% were left-handed (L)
• 47% were Democrats (D)
• If a president is left-handed, there is a 13% chance that the president is a Democrat.

Based on this information on the last fifteen U.S. presidents, is "being left-handed" independent of "being a Democrat"?

1. Yes, since 0.47 is not equal to 0.13.
2. Yes, since 0.40 * 0.47 is not equal to 0.13.
3. No, since 0.47 is not equal to 0.13.
4. No, since 0.40 is not equal to 0.13.

Question 5

If P(A) = 0.35, P(B) = 0.13, and P(A and B) = 0.12, then P(A|B) =.

(Please round to two decimal places.)

Question 6

If P(A) = 0.32, P(B) = 0.46, and P(A or B) = 0.75, then P(A|B) =.

(Please round to two decimal places.)

Question 7

A hair salon surveyed 377 customers (130 females and 247 males) to see if they are satisfied with the service. The result is summarized in the following table.

Satisfied

Not Satisfied

Total

Female

102

28

130

Male

230

17

247

Total

332

45

377

1. If a customer is randomly selected from these 377 people, the probability that he/she is satisfied is.

(Please round your answer to two decimal places.)

2. If we know the selected customer is a female, then what is the probability that she is satisfied?

(Please round your answer to two decimal positions.)

P(satisfied|female) =

3. How about the probability that a randomly selected customer is a female if we know that the person is satisfied?

(Please round your answer to two decimal positions.)

P(female|satisfied) =

Question 8

At a dental office, the probability a patient needs a cleaning is 0.71. The probability a patient needs a filling is 0.19. Assuming the events "needs a cleaning" and "needs a filling" are independent, then what is the probability a patient needs a filling given that he/she needs a cleaning?

1. 0.4
2. 0.13
3. Additional information is required to determine the probability.
4. 0.19
5. 0.71

Question 11

Dogs are inbred for such desirable characteristics as blue eye color, but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported inThe Dalmatians Dilemma) found the following:

(i)

31% of all Dalmatians have blue eyes.

(ii)

38% of all Dalmatians are deaf.

(iii)

If a Dalmatian has blue eyes, there is a 42% chance that it is deaf.

What is the probability that a randomly chosen Dalmatian is blue-eyedanddeaf?

1. 0.31 * 0.38 = 0.1178
2. 0.31 * 0.42 = 0.1302
3. 0.38 * 0.42 = 0.1596
4. 0.31/0.38 = 0.8158
5. 0.31/0.42 = 0.7381
6. 0.38/0.42 = 0.9048

Question 12

Suppose that the handedness of the last 15 U.S. presidents is as follows:

(i)

40% were left-handed (L)

(ii)

47% were democrats (D)

(iii)

If a president is left-handed, there is a 13% chance that the president is a Democrat.

What is the probability that a randomly chosen U.S. president is left-handed and a democrat?

1. 0.40 * 0.47 = 0.1880
2. 0.40 * 0.13 = 0.0520
3. 0.47 * 0.13 = 0.0611
4. 0.40/0.47 = 0.8510
5. 0.40/0.13 = 3.0769
6. 0.47/0.13 = 3.6154

Question 13

Suppose a basketball team had a season of games with the following characteristics:

Of all the games, 57% were at-home games. Denote this by H (the remaining were away games).

Of all the games, 34% were wins. Denote this by W (the remaining were losses).

Of the at-home games, 28% of games were wins.

Of all the games,% of games were at-home wins. (Please round your answer to one decimal place.)