Question

three persons a, b and c draw in succession from a bag containing 8 red and 4 white balls until a white ball is drawn. what is the probability that c draws the white ball?

Answer 1

Three balls are drawn from a bag containing 5 white, 4 black and 6 red balls. Find the probability that all the balls are of one colors?  Let's find the probabilities of all balls being white, black & red independently & then add them to get the final probability.  Probability of getting first ball white = 5/15 = 1/3. Probabilities of getting 2nd & 3rd ball white are 4/14 = 2/7 & 3/13 respectively.  Applying Bayes theorem, Probability of getting all white balls = 1 × 2 × 3 / 3 × 7 × 13            = 2/91.  Repeat the same procedure to find the other 2 probabilities, add them & get the final probability.   Ans. = 2/91 + 4/455 + 4/91          = 34/455.