Question

In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is :

(1) 11/16

(2) 13/16

(3) 9/16

(4) 15/16

Answer 1

Answer is (1) 11/16

A : Event when card A is drawn

B : Event when card B is drawn.

P(A) = P(B) = 1/2

Required probability = P(AA or (AB)A

or (BA)A or (ABB)A or (BAB)A or (BBA)A)

= 1/2 x 1/2 + (1/2 x 1/2 x 1/2) x 2 + (1/2 x 1/2 x 1/2 x 1/2) x 3

= 1/4 + 1/4 + 3/16 = 11/16