Question

oints A random sample of adult drivers was obtained 52% men and 46% women. A survey showed that s rivers are women and use GPS. Suppose a person included in this survey is randomly selected of the drivers rely on GPS systems 28% of the drivers are men and use GP while 2 % of 0.5 pts.) 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. Submit Answer Incorrect. Tries 3/S Previous Tries 0.5 pts.) Please show your work for above part here Submission type: Submit entries below as answer to receive credit Save entries below (not submitted for credit yet) Submit Answer Tries 0/s 0.5 pts.) 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 Submit Anewer Tries o/5 0.5 pts.) Please show your work for above part here

Part A and B

Answer 1

Let M shows the event that person is man and W shows the event that person is woman. So we have

P(M) = 0.52, P(W) = 0.46

Let G shows the event that person uses GPS. So we have

P(G) = 0.58, P(G') = 1 - P(G) = 1 - 0.58 = 0.42

And we have

P(G and M) = 0.28, P(G and W) = 0.24

(a)

The probability that person relies on a GPS system, given that person has man is

P(G | M) = P(G and M) / P(M) = 0.28 / 0.52 = 0.5385

Answer: 0.5385

(b)

The probability that the person is a woman, given that person relies on GPS is

P(W | G) = P(G and W) / P(G) = 0.24 / 0.58 = 0.4138

Answer: 0.4138