Question #346453

Off-road motorbike racing can be dangerous, especially when it rains. It has been found that it rains during



18% of races. When it does not rain, there is a 5% chance that Dwayne (a rider) will get hurt. However, when it



rains, the chance that he gets hurt increases to 35%. Dwayne has just finished a race and is hurt. What is the



probability that it rained during the race?

1
Expert's answer
2022-05-31T13:50:34-0400

Let RR denote the event "rain during race". Let HH denote the event " a rider will get hurt".

Given P(R)=0.18,P(HR)=0.35,P(HRC)=0.05.P(R)=0.18, P(H|R)=0.35, P(H|R^C)=0.05.


P(RH)=P(R)P(HR)P(R)P(HR)+P(RC)P(HRC)P(R|H)=\dfrac{P(R)P(H|R)}{P(R)P(H|R)+P(R^C)P(H|R^C)}

=0.18(0.35)0.18(0.35)+(10.18)(0.05)0.6058=\dfrac{0.18(0.35)}{0.18(0.35)+(1-0.18)(0.05)}\approx0.6058


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