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. If the next draw of a ball from this bag will give a white ball then the probability that the drawn of four balls initially contain two white and two red balls.

Answer 1

A bag contains $6$ red and $4$ white balls

$P(2$ red balls $\xi$ $2$ white balls $)$

$\Rightarrow \frac{{}^6{C}_2{}^4{C}_2}{{}^{10}{C}_4}=\frac{6\times 15}{210}=\frac{15}{14}$

Total outcomes ${}^{10}{C}_4$

Hence, the answer is ${}^{10}{C}_4.$