Question

Two of the most popular options on a certain type of new car are automatic transmission and built-in GPS. Suppose that 90% of all buyers request automatic transmission, 82% of all buyers request built-in GPS, and 77% of all buyers request both automatic transmission and built-in GPS. Hint: It may be useful to draw Venn diagrams for these. What is the probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS

Answer 1

0.95 = 95% probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS

Explanation:

We solve this question treating these probabilities as Venn sets.

I am going to say that:

Event A: Requesting automatic transmission

Event B: Requesting built-in GPS

90% of all buyers request automatic transmission

This means that
`P(A) = 0.9`

82% of all buyers request built-in GPS

This means that
`P(B) = 0.82`

77% of all buyers request both automatic transmission and built-in GPS.

This means that
`P(A \cap B) = 0.77`

What is the probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS

This is
`P(A \cup B)`, which is given by:

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

So

`P(A \cup B) = 0.9 + 0.82 - 0.77 = 0.95`

0.95 = 95% probability that the next person to purchase this car will request at least one of automatic transmission or built-in GPS