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?\n-0.08\n-0.04\n0.2\n0.4

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?\n-0.08\n-0.04\n0.2\n0.4

Answer

Explanation:

Step1: Calculate the probability of drawing a black chip and a red chip

There are a total of (2 + 3=5) chips. 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 the expected value for one draw

The expected value for one draw (E(X)) is given by the formula (E(X)=\sum_{i}x_{i}P(x_{i})) For a black chip (x = 2), for a red chip (x=- 1) (E(X)=2\times\frac{2}{5}+(-1)\times\frac{3}{5}=\frac{4 - 3}{5}=\frac{1}{5}=0.2)

Step3: Calculate the expected value for two - draw rounds (since chips are replaced)

Since the draws are independent, for two - draw rounds, the expected value (E = 2\times E(X)) (E = 2\times0.2=0.4)

Answer:

(0.4)