A random sample of adult drivers was obtained where 52% were men and 46% were women. Note that everyone is not classified as a man or a women. A survey showed that 65% of the drivers rely on GPS systems. 30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected. a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places. b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places. c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places. d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places. e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.

a) P(G | M) = 0.577

b) P(W | G) = 0.523

c) P(M and G') = 0.220

d) P(M or G) = 0.870

e) P(G') = 0.350

Step-by-step explanation:

A random sample of adult drivers was obtained where 52% were men and 46% were women.

P(M) = 0.52

P(W) = 0.46

A survey showed that 65% of the drivers rely on GPS systems.

P(G) = 0.65

30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS.

P(M and G) = 0.30

P(W and G) = 0.34

a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places

P(G | M) = ?

Recall that conditional probability is given by

∵ P(B | A) = P(A and B)/P(A)

For the given case,

P(G | M) = P(M and G)/P(M)

P(G | M) = 0.30/0.52

P(G | M) = 0.577

b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.

P(W | G) = ?

Recall that conditional probability is given by

∵ P(B | A) = P(A and B)/P(A)

For the given case,

P(W | G) = P(W and G)/P(G)

P(W | G) = 0.34/0.65

P(W | G) = 0.523

c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.

P(M and G') = ?

Where G' means does not rely on a GPS system

P(M and G') = P(M) - P(M and G)

P(M and G') = 0.52 - 0.30

P(M and G') = 0.220

d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.

P(M or G) = ?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(M or G) = P(M) + P(G) - P(M and G)

P(M or G) = 0.52 + 0.65 - 0.30

P(M or G) = 0.870

e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.

P(G') = ?

P(G') = 1 - P(G)

P(G') = 1 - 0.65

P(G') = 0.350

question

what is the value of the third quartile of the data set represented by this box plot? a. 19 b. 21 c. 26 d. 29

answer

c