Let XXX and YYY be independent with X∼Exp(λ1)X \sim \text{Exp}(\lambda_1)X∼Exp(λ1) and Y∼Exp(λ2)Y \sim \text{Exp}(\lambda_2)Y∼Exp(λ2) where λ1≠λ2\lambda_1 \ne \lambda_2λ1=λ2. What is P(X<Y)P(X < Y)P(X<Y)?
λ1λ1+λ2\frac{\lambda_1}{\lambda_1+\lambda_2}λ1+λ2λ1
λ2λ1+λ2\frac{\lambda_2}{\lambda_1+\lambda_2}λ1+λ2λ2
12\frac{1}{2}21
λ1λ2(λ1+λ2)2\frac{\lambda_1\lambda_2}{(\lambda_1+\lambda_2)^2}(λ1+λ2)2λ1λ2