Probability statistics

Question

Bicycles for hire at the Beach front are deemed beyond repair when one or both its

wheels are damaged. According to current statistics, there is an 8% chance that the front wheel

gets damaged and a 12% chance the back wheel gets damaged.

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 us first define the variables in this problem.

F = front wheel is damaged

B = back wheel is damaged

F’ = front wheel is not damaged

B’ = back wheel is not damaged

P(F) = .08

P(B) = .12

P(F’) = .92

P(B’) = .88

The probability that the bike is beyond repair is made up of three different cases. Since these events are all independent we can multiply their probabilities together.

P(F, B) = (.08)(.12) = .0096

P(F’, B) = (.92)(.12) = .1104

P(F, B’) = (.08)(.88) = .0704

When we add up the total of these three cases we get the probability that the bike is beyond repair.

.0096 + .1104 + .0704 = .1904