Question

A bag contains $8$ red and $5$ white balls. Three balls are drawn at random. Find the probability that one ball is red and two balls are white.

• A. $\frac{40}{143}$
• B. $\frac{40}{147}$
  
• C. $\frac{41}{141}$
  
• D. $\frac{39}{147}$

Answer 1

The correct option is A $\frac{40}{143}$

We have $8$ red and $5$ white balls. total $=13$

A total of $3$ balls are to be selected.

So total outcomes $=$ ${{}^{13}C}_3$

Favourable outcomes $=$ selection of $1$ red and $2$ white balls = ${{}^{8}C}_1\times {{}^{5}C}_2$

So probability, $p=\frac{{{}^{8}C}_1\times {{}^{5}C}_2}{{{}^{13}C}_3}=\frac{40}{143}$