Question

4. In a box are 3 red balls and 5 blue balls. From this box are drawn 4 balls and placed in a second box. Then, one ball is drawn from the second box. What is the probability the ball drawn from the second box is red?

please so detailed steps

Answer 1

P( ball drawn from second box is red)

= P( ball drawn from second box is red | 3 red balls have drawn from first box) * P(3 red balls have drawn from first box) + P( ball drawn from second box is red | 2 red balls have drawn from first box) * P(2 red balls have drawn from first box) + P( ball drawn from second box is red | 1 red ball has drawn from first box) * P(1 red ball has drawn from first box)

$=\frac{3}{4}*\frac{\binom{3}{3}*\binom{5}{1}}{\binom{8}{4}} + \frac{2}{4}*\frac{\binom{3}{2}*\binom{5}{2}}{\binom{8}{4}} + \frac{1}{4}*\frac{\binom{3}{1}*\binom{5}{3}}{\binom{8}{4}}$

$=\frac{3*1*5}{4*70} + \frac{2*3*10}{4*70} + \frac{3*10}{4*70}$

$= 0.0535714 + 0.214286 + 0.107143$

$= 0.375$