Question

two black chips and three red chips are put into a bag. two points are awarded for each black chip drawn, and one point is lost for each red chip drawn. what is the expected value for each round if there are two draws per round and the chips are replaced after each draw?
-0.08
-0.04
0.2
0.4

Explanation:

Step1: Define probabilities and values

Total chips: $2+3=5$. Probability of black chip: $P(B)=\frac{2}{5}$, value of black chip: $V(B)=2$. Probability of red chip: $P(R)=\frac{3}{5}$, value of red chip: $V(R)=-1$.

Step2: Calculate single draw expected value

Expected value for 1 draw: $E_1 = P(B) \times V(B) + P(R) \times V(R)$
$E_1 = \frac{2}{5} \times 2 + \frac{3}{5} \times (-1) = \frac{4}{5} - \frac{3}{5} = \frac{1}{5} = 0.2$

Step3: Calculate two draws expected value

Since draws are independent, total expected value: $E = 2 \times E_1$
$E = 2 \times 0.2 = 0.4$

Answer:

0.4