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.

Answer 1

The expected value for each round, if there are two draws per round and the chips, are replaced after each draw is 0.4.

Given to us

Number of black chips = 2

Number of red chips = 3

Points are given for a black chip = +2

Points are given for a red chip = -1

What are the probabilities of the different cases?

We know that for each round there will be 2 draws, therefore, there will be four cases,

Case1:

Probability, when both the chips drawn are black,

$\dfrac{2}{5} \times \dfrac{2}{5} = \dfrac{4}{25}$

Case2:

Probability, when the first chip is black and the next chip is red,

$\dfrac{2}{5}\times \dfrac{3}{5}=\dfrac{6}{25}$

Case 3:

Probability, when the first chip is red and the next chip is black,

$\dfrac{3}{5}\times \dfrac{2}{5}=\dfrac{6}{25}$

Case 4,

Probability, when both the chips drawn are red,

$\dfrac{3}{5}\times \dfrac{3}{5}=\dfrac{9}{25}$

What is the expected value for each round?

The expected value of each round can be found,

$E(x) = (2+2)\dfrac{4}{25} + (2-1)\dfrac{6}{25} +(-1+2)\dfrac{6}{25} +(-1-1)\dfrac{9}{25}$

E(x) = 0.4

Hence, the expected value for each round, if there are two draws per round and the chips, are replaced after each draw is 0.4.

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