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: Calculate probability of drawing each type of chip

The total number of chips is $2 + 3=5$. The probability of drawing a black chip $P(B)=\frac{2}{5}$ and the probability of drawing a red chip $P(R)=\frac{3}{5}$.

Step2: Calculate expected - value of a single draw

The value of drawing a black chip is $2$ and the value of drawing a red chip is $- 1$. The expected - value of a single draw $E(X)$ is given by $E(X)=2\times\frac{2}{5}+(-1)\times\frac{3}{5}=\frac{4 - 3}{5}=\frac{1}{5}=0.2$.

Step3: Calculate expected - value of two draws

Since the draws are independent and the chips are replaced after each draw, the expected - value of two draws is $E(2X)=2\times E(X)$. Substituting the value of $E(X) = 0.2$, we get $E(2X)=2\times0.2 = 0.4$.

Answer:

0.4