3.1 Problems

3.1.1 Gain-loss

A bag has 4 green and 6 black balls. 3 balls are drawn randomly. Choosing a green ball brings 10 tk gain, while a black one takes away 5 tk. What is the expected gain?

Solution

Green Balls	Black Balls	Gain (\(x\)) Tk)	Probability \(p(x)\)
3	0	\(3 \times 10 + 0 \times (-5) = 30\)	\(\frac{1}{30} \approx 0.0333\)
2	1	15	\(\frac{9}{30} = 0.3\)
1	2	0	\(\frac{15}{30} = 0.5\)
0	3	-15	\(\frac{5}{30} \approx 0.1667\)