Question

An urn A contains 4 white and 6 red balls. Three balls are drawn at random the expected number of red balls drawn is

• A. 3
• B. 1.8
• C. 1.2
• D. 1.6

Answer 1

The correct option is B 1.8

Total number of balls: 4 White and 6 Red $=$ 10 balls
Cases for three balls are drawn at random:
Selection of 3 balls from 10 balls ${=}^{10}{C}_3$
Case A: 1 Red and 2 White $=\frac{{}^6{C}_1{\times }^4{C}_2}{{}^{10}{C}_3}=\frac{36}{120}$
Case B: 2 Red and 1 White $=\frac{{}^6{C}_2{\times }^4{C}_1}{{}^{10}{C}_3}=\frac{60}{120}$
Case C: 3 Red and 0 White $=\frac{{}^6{C}_3{\times }^4{C}_0}{{}^{10}{C}_3}=\frac{20}{120}$
Expected number of red balls drawn is $=1\times Case\left(A\right)+2\times Case\left(B\right)+3\times Case\left(C\right)$
$=\frac{36}{120}+2\times \frac{60}{120}+3\times \frac{20}{120}$
$=\frac{9}{5}=1.8$