Question

A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white balls, 4 red balls and 5 black balls.

• A. $\frac{90}{648}$
• B. $\frac{558}{648}$
• C. $\frac{82}{648}$
• D. $\frac{566}{648}$

Answer 1

The correct option is C $\frac{82}{648}$

$B_1$	$B_2$	$B_3$
1W 3R 2B	2W 3R 4B	3W 4R 5B

P(WWW + RRR + BBB)

$=(\frac{1}{6}\times \frac{2}{9}\times \frac{3}{12})+(\frac{3}{6}\times \frac{3}{9}\times \frac{4}{12})+(\frac{2}{6}\times \frac{4}{9}\times \frac{5}{12})$

$=\frac{6+36+40}{648}=\frac{82}{648}$