Let S = w 1 , w 2 , … . be the sample space associated to a random experiment. Let P w n = P w n - 1 2 , n ≥ 2 . Let A = 2 k + 3 l ; k , l ∈ ℕ and B = w n ; n ∈ A . Then P B is equal to

Step-by-step solution

Given, P w n = P w n - 1 2 ,   n ≥ 2 Let P w 1 = λ then P w 2 = λ 2   P w 3 = λ 2 2         ⋮         ⋮         ⋮         ⋮         ⋮         ⋮ P w n = λ 2 n - 1 As ∑ k = 1 ∞ P w k = 1 ⇒ λ + λ 2 + λ 2 2 + λ 2 3 + . . . . = 1 ⇒ λ 1 - 1 2 = 1 ⇒ λ = 1 2 So, P w n = 1 2 n