two black chips and three red chips are put into a bag. two points are awarded for each black chip drawn…

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

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

Answer

Explanation:

Step1: Calculate probability of drawing black chip

Total chips = 2 + 3 = 5. Probability of drawing a black chip $P(B)=\frac{2}{5}$, probability of drawing a red chip $P(R)=\frac{3}{5}$.

Step2: Calculate expected - value of one draw

The value of drawing a black chip is 2 points and a red chip is - 1 point. Expected - value of one draw $E(X)=2\times\frac{2}{5}+(-1)\times\frac{3}{5}=\frac{4 - 3}{5}=\frac{1}{5}=0.2$.

Step3: Calculate expected - value of two draws

Since the draws are independent and with replacement, the expected - value of two draws is $E = 2\times E(X)$. Substitute $E(X)=0.2$ into the formula, we get $E = 2\times0.2 = 0.4$.

Answer:

0.4