Answer to Question #127468 in Statistics and Probability for Honey

Question

Q.No.5: A bag contains 14 identical balls, 4 of which are red, 5 black and 5 white. Six balls are drawn from the bag. Find the probability that:

(i) 3 are red, (ii) at least two are white

Answer 1

Here is a hypergeometric distribution. Selections are made without replacing.

(I)

Success group consists of 4 red balls. There was 6 draws.

The probability to pull 3 red balls is $C_4^3 \cdot C_{10}^3/C_{14}^6 \approx 0.16$

(II)

Success group consists of 5 white balls. There was 6 draws.

The probability to pull 0 white balls is $C_5^0 \cdot C_{9}^6/C_{14}^6 \approx 0.028$

The probability to pull 1 white ball is $C_5^1 \cdot C_{9}^5/C_{14}^6 \approx 0.21$

The probability to pull at least 2 white balls is $1-0.028-0.21=0.762$