Question

Consider the following game. There is a bottle with 20 colored chips inside. There are 2 blue chips, 4 purple chips, 7 green chips, and 7 red chips. You pay $2 and pick one out at random. If you pick a blue chip, you get a prize of $10. If you pick a purple chip, you get a prize of $5. You get nothing for red or green chips. What is the expected value of playing the game?

Answer 1

Answer: Expected value of playing the game is $0.

Step-by-step explanation:

Since we have given that

Total number of colored chips = 20

Number of blue chips = 2

Number of purple chips = 4

Number of green chips = 7

Number of red chips = 7

Amount of prize he gets for blue chip = $10

Amount of prize he gets for a purple chip = $5

No amount is given for red or green

Amount he had to pay = $2

So, Expected value of playing the game is given by

$\frac{2}{20}\times 10+\frac{4}{20}\times 5+7\times 0+7\times 0-2\\\\=1+1-2\\\\=2-2\\\\=\ 0$

Hence, Expected value of playing the game is $0.

Answer 2

Answer: $0

Step-by-step explanation:

Given : Total colored chips  in the bottle= 20

No. of blue chips = 2

Probability of getting blue chip= $\dfrac{2}{20}=0.1$

Prize for blue chip = $10

No. of purple chips = 4

Probability of getting purple chip= $\dfrac{4}{20}=0.2$

Prize for purple chips = $5

No. of green chips = 7

No.of red chips = 7

Probability of getting green chip or red chip= $\dfrac{7+7}{20}=0.7$

Price for green or red chip = 0

Amount you paid to play the game = $2

Then , the expected value of playing the game will be :-

$0.1\times\ 10+0.2\times\ 5+0.7\times\ 0-\ 2\\\\=\ 1+\ 1-\ 2=\ 0$

Hence, the expected value of playing the game = $0