Question

A car producer stocks three types of tires: A, B, and C. Let P(A) = 0.40, P(B) = 0.15 and P(C) = 0.45. The percentage of defective tires is 2%, 1% and 5%, respectively.

Someone picks a tire off the shelf at random and it is Brand A.
If you want to know the probability that it is a defective tire (event D), which formula would you use? If you want to know the probability that it is a defective tire (event D), which formula would you use?
a) P(AD)= PD AP(A) PD)
b) P(D|A) = P(A|DP(D) P(A)
c) P(AD)= PD APD) P(A)
d) P(DA)= P(ADP(A) PD)

Answer 1

The correct option is b)
`P(D|A)=P(A|D)P(D)`.

Explanation:

The probability of selecting the different types of tires are:

P (A) = 0.40

P (B) = 0.15

P (C) = 0.45

The defective rate for the different types of tires are:

P (D|A) = 0.02

P (D|B) = 0.01

P (D|C) = 0.05

The formula to compute the probability that the tire is defective given that it is Brand A tire as follows:

`P(D|A)=P(A|D)P(D)`