Question #339042

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
2022-05-10T06:59:22-0400

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

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

As the two events are independent


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

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


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

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

=0.08+0.120.08(0.12)=0.1904=0.08+0.12-0.08(0.12)=0.1904


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