Question

An unbiased dice is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is 

(A) 1/2 

(B) 2/5 

(C) 1/5 

(D) 2/3

Answer 1

Answer is (B) 2/5

Probability of success = 2/6 = 1/3 = p

Probability of failure = 1 - 1/3 = 2/3 = q

Probability that success occurs in even number of tosses

= P(FS) + P(FFFS) + P(FFFFFS) +  .... = pq + q³p + q⁵p + ..... = pq/(1 - q²) = 2/5