Question

Bicycles for hire at the Durban 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 A denote front wheel damaged

So P(A)=0.08

and B denote that back wheels get damaged

so P(B)=0.12

As the two events are independent

$P(A\cap B)=P(A).P(B)=0.08\times 0.12=0.0096$

Probability that hired bike will deemed beyond repair-

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

$=0.08+0.12-0.0096=0.1904$