Question

A bag contains ‘m’ white and ‘n’ black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after draw. A beings the game. If the probability of A wining (that is drawing a white ball) is twice the probability of B wining, then the ratio mn is equal to:

Solution

Correct option is

1: 1

Ai = A wins in ith try

Bi = B wins in ith try

⇒ P(A wins) = P(A wins in 1st attempt) + P(A wins in 2ndattempt)+…..∞                        

              

                   

               

The above series is a G.P. with infinite terms, where common ratio 

⇒ P(B wins) = 1 – P(A wins)        (∵ There is no possible of draw)

                               

It is given that P(A) = 2P(B)   

SIMILAR QUESTIONS

Q1

An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is:

Q2

If ten objects are distributed at random among ten persons, the probability that at least one of them will not get object is:

Q3

If two events A and B are such that 

                       

Q4

One ticket is selected at random from 100 tickets numbered 00, 01, 02,…99. Suppose A and B are the sum and product of the digits found on the ticket. Then P(A = 7/8 = 0) is given by:

Q5

A box contain 100 tickets numbered 1, 2,…100. Two tickets are chosen at random. It is given that the greater number on the two chosen tickets is not more than 10. The probability that the smaller number is 5 is:

Q6

A bag contains four tickets marked with numbers 112, 121, 211, 222. One ticket is drawn at random from the bag. Let

Ei(i = 1, 2, 3) denote the event that its digit on the ticket is 2. Than:

Q7

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is:

Q8

There are 20 cards. 10 of these cards have the letter ‘I’ printed on them and the other 10 have the letter ‘T’ printed on them. If three cards are drawn without replacement and kept in the same order, the probability of making word IIT is:

Q9

A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till the balls are drawn from the boxes. The probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red is:

Q10

If X is a binomial variate with parameters n and p, where 0 < p < 1 such that  is independent of n and r, then p equals: