Question

(5 points) A random sample of adult drivers was obtained where 50% were men and 49% were women. Note that everyone is not classified as a man or a woman. A survey showed that 77% of the drivers rely on GPS systems. 38% of the drivers are men and use GPS while 38% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected. (0.5 pts.) a) Suppose the person selected is a man. What is the probability that he relies on a GPS system

Answer 1

the probabiility that the selected man relies on a GPS system is 0.494

Explanation:

From the given information:

Let X be the event that selected person is a man

Let Y be the event that selected person is a woman

Let Z be the event that selected relies or use GPS system.

So;

the following probabilities are:

P(X) = 0.50

P(Y) = 0.49

P(Z) = 0.77

P(X ∩ Z) = 0.38

P(Y ∩ Z) = 0.38

Now;

if the selected person is a man, the probability that he relies on a GPS system can be determined as follows:

`P(Z|X) = (P(X \cap Z))/(P(Z))`

`P(Z|X) = (0.38)/(0.77)`

`\mathbfP(Z`

Thus, the probabiility that the selected man relies on a GPS system is 0.494