Question

A bag contains $5$ red and $3$ blue balls. If $3$ balls are drawn at random without replacement, then the probability of getting exactly two red balls is

$\left(a\right)\frac{5}{14}\left(b\right)\frac{5}{28}$
$\left(c\right)\frac{5}{7}\left(b\right)\frac{15}{28}$

Answer 1

The probability of getting exactly two red $(R_1,R_2$) balls $=(P_{R_1}\times P_{R_2}\times P_B)+(P_{R_1}\times P_B\times P_{R_2})+(P_B\times P_{R_1}\times P_{R_2})$
$=(\frac{5}{8}\times \frac{4}{7}\times \frac{3}{6})+(\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6})+(\frac{3}{8}\times \frac{5}{7}\times \frac{4}{6})=\frac{15}{28}$