Answer to Question #193448 in Statistics and Probability for Olwethu

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-

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

$=0.08+0.12-0.0096=0.1904$