Question

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is 1/3, then the probability that the experiment stops with head is

(A) 1/3

(B) 5/21

(C) 4/21

(D) 2/7

Answer 1

Correct option is (B) 5/21

P(H) = \(\frac 13\)

P(T) = \(\frac 23\)

P(E) = P(HH) + P(THH) + P(HTHH) + P(THTHH) + P(HTHTHH) + P(THTHTHH) + .....