Question

A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is

• A. $\frac{3}{8}$
• B. $\frac{2}{15}$
• C. $\frac{15}{28}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{15}{28}$

$Box\to 5Black,3Red$

$P(2B,1R)=P(B,B,R)+P(B,R,B)+p(R,B,B)$

$=\frac{5}{8}\times \frac{4}{7}\times \frac{3}{6}+\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6}+\frac{3}{8}\times \frac{5}{7}\times \frac{4}{6}$

$=3\times \frac{5\times 4\times 3}{8\times 7\times 6}$

$P(2B,1R)=\frac{15}{28}$