Question

Suppose a box contains 1500 balls out of which 7500 are white and the remaining are black balls. if we draw a sample 8 balls randomly (with out replacement). What is the probability that they are all white ball?

Answer 1

We can use the hypergeometric distribution to solve this problem.

The total number of balls in the box is N = 1500, out of which n = 7500 are white and N - n = 7500 are black. We want to know the probability of drawing a sample of k = 8 balls that are all white without replacement.

The probability of drawing the first white ball is n/N = 7500/1500 = 0.5.

The probability of drawing the second white ball, without replacement, is (n-1)/(N-1) = 7499/1499.

Following the same reasoning, the probability of drawing 8 white balls, without replacement, is:

P(8 white balls) = (n/N) * ((n-1)/(N-1)) * ((n-2)/(N-2)) * ... * ((n-7)/(N-7))

= (7500/1500) * (7499/1499) * (7498/1498) * ... * (7493/1493)

= 0.0444 (rounded to four decimal places)

Therefore, the probability of drawing a sample of 8 balls that are all white without replacement from a box containing 1500 balls of which 7500 are white is 0.0444.