There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. What is the probability that 7th drawn ball is 4th white ball ?

To find: The probability that the 7th ball drawn is the 4th white ball. Solution: Probability of getting a white ball per draw is 1/2. Probability of getting a red ball per draw is 1/2. As the balls are replaced after every draw, this probability does not change. Now for a clear understanding let us consider each draw as an event. there are total seven events. _ _ _ _ _ _ _. For the seventh event to be a white ball, the previous six events should contain 3 white balls and 3 red balls in any random arrangement. The number of ways for this is 6C3 (1/2)^3 * (1/2)^3 [6C3 is the number of ways to select 3 places out of 6 places. (1/2)^3 is probability of getting 3 white balls and the second (1/2)^3 is the probability of getting three red balls]. = [(6*5*4)/(3*2*1)] * (1/64) = 5/16. Now for the seventh ball to be white the probability is 1/2. So, total probability = (5/16)*(1/2) = 5/32 read less