Answer to Question #339042 in Statistics and Probability for Pumpkin

Question

What is the probability that a hired bike will be deemed beyond repair provided that the wheels get damaged independently of each other

Answer 1

Let A denote front wheel damaged. So $P(A)=0.08$

Let B denote that back wheels get damaged. So $P(B)=0.12.$

As the two events are independent

$$P(A\cap B)=P(A)P(B)$$

The probability that a hired bike will be deemed beyond repair  is

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

$$=P(A)+P(B)-P(A)P(B)$$

$$=0.08+0.12-0.08(0.12)=0.1904$$