Let S= w1, w2, ldots. 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

Question

Let S= w1, w2, ldots. 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 (A) (3/32) (B) (3/64) (C) (1/16) (D) (1/32)

Tardigrade Admin · Accepted Answer

Let P ( w 1)=λ then P ( w 2)=(λ/2) ldots P ( w n )=(λ/2 n -1) As displaystyle∑ k =1∞ P ( w k )=1 ⇒ (λ/1-(1)2)=1 ⇒ λ=(1/2) So, P ( w n )=(1/2 n ) A = 2 k +3 ℓ ; k , ℓ ∈ N = 5,7,8,9,10 ldots . . B = w n: n ∈ A B = w 5, w 7, w 8, w 9, w 10, w 11, ldots . A = N - 1,2,3,4,6 ∴ P ( B )=1-[ P ( w 1)+ P ( w 2)+ P ( w 3)+ P ( w 4)+ P ( w 6)] =1-[(1/2)+(1/4)+(1/8)+(1/16)+(1/64)] =1-(32+16+8+4+1/64)=(3/64)

Q. Let $S = {w_{1}, w_{2}, \dots .}$ be the sample space associated to a random experiment. Let $P (w_{n}) = \frac{P ( w _{n - 1} )}{2}, n \geq 2$ . Let $A = {2 k + 3 ℓ; k, ℓ \in N}$ and $B = {w_{n}; n \in A}$ . Then $P (B)$ is equal to

$\frac{3}{32}$

$\frac{3}{64}$

$\frac{1}{16}$

$\frac{1}{32}$

Q. Let S={w1​,w2​,….} be the sample space associated to a random experiment. Let P(wn​)=2P(wn−1​)​,n≥2. Let A={2k+3ℓ;k,ℓ∈N} and B={wn​;n∈A}. Then P(B) is equal to

323​

643​

161​

321​

Q. Let $S = {w_{1}, w_{2}, \dots .}$ be the sample space associated to a random experiment. Let $P (w_{n}) = \frac{P ( w _{n - 1} )}{2}, n \geq 2$ . Let $A = {2 k + 3 ℓ; k, ℓ \in N}$ and $B = {w_{n}; n \in A}$ . Then $P (B)$ is equal to

$\frac{3}{32}$

$\frac{3}{64}$

$\frac{1}{16}$

$\frac{1}{32}$