Question #193448

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? 


1
Expert's answer
2021-05-17T13:57:19-0400

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



Probability that hired bike will deemed beyond repair-


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


=0.08+0.120.0096=0.1904=0.08+0.12-0.0096=0.1904


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