Question-27
The total duration of a Test cricket match between any two cricket team is uniformly distributed between 90 overs and 450 overs, both inclusive. What is the probability that the duration of a test cricket match between two cricket team is more than 400 overs? Enter the answer correct two decimal places.
If \(X \sim \text{Uniform}[a,b]\), then \(E(X) = \dfrac{a+b}{2}\) and \(Var(X) = \dfrac{(b-a)^{2}}{12}\). Also,
\(F(x) = P(X \leq x) = \dfrac{x-a}{b-a}\)
\(P(X > x) = 1-P(X \leq x) = 1- \left(\dfrac{x-a}{b-a}\right).\)
0.14
According to the question \(X \sim \text{Uniform}[90, 450]\).
Prob.[the duration of a test cricket match between two cricket team is more than 400 overs]
\(\implies P\left(X > 400\right) = 1 - P\left( X \leq 400\right)\)
\(= 1 - \left(\dfrac{400-90}{450-90}\right)\)
\(= 1- \dfrac{310}{360}\)
\(\implies 1-\dfrac{31}{36} = \dfrac{5}{36} = 0.14\)