Question

bag contains 10 white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. Find the probability that all black balls are drawn by the 6thdraw.
Plz answer..

Answer 1

Solution:

By Hypergeometric Distribution:

where k=6 , M=13 , n=3, x=3

P[all blacks]= ((k taken x)(M-k taken n-x))/(M taken n)
P[all blacks]= ((6 taken 3)(13-6 taken 3-3))/(13 taken 3)
P[all blacks]= ((6 taken 3)(7 taken 0))/(13 taken 3)
P[all blacks]= ((20)(1))/(286)
P[all blacks]= 0.0699

Therefore, by heypergeometric distribution the probability that all black balls are drawn by the 6th draw is 0.0699.