Question

A bag contain 6 Red and 4 White balls. 4 balls are drawn one by one without replacement and were found to be atleast 2 white. Then the probability that next draw of a ball from this bag will give a white ball.

Answer 1

Given:

Total number of balls = 6+4=10

4 balls drawn, possible scenarios are,

(i) 2 white, 2 red ball - 2 white balls left and 4 red balls left, hence next draw to be white in this scenario= $\frac{2}{6}$

(ii) 3 white balls, 1 red balls - 1 white ball left and 5 red balls left, hence next draw to be white in this scenario = $\frac{1}{6}$

(iii) 4 white balls, 0 red balls - 0 white balls left and 6 red balls left, hence next draw to be white in this scenario = $\frac{0}{6}$

Hence, the probability that next draw of a ball from this bag will give a white ball.= case (i) or case (ii) or case (iii) = $\frac{2}{6}+\frac{1}{6}+\frac{0}{6}=\frac{3}{6}=\frac{1}{2}$