Question

A bag contains 10 blue marbles, 3 yellow marbles, and 12 orange marbles. If a blue marble is drawn you win $10. If a yellow marble is drawn you win $15. if an orange marble is drawn you lose $10. it cost $1 to play. Should you play the game?

Answer 1

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.

Explanation:

Given - A bag contains 10 blue marbles, 3 yellow marbles, and 12 orange marbles. If a blue marble is drawn you win $10. If a yellow marble is drawn you win $15. if an orange marble is drawn you lose $10. it cost $1 to play.

To find - Should you play the game?

Formula used -

Expected value , E[x] = ∑x p(x)

where p(x) is the probability.

Proof -

Given that,

Total blue marbles in a bag = 10

Total yellow marbles in a bag = 3

Total orange marbles in a bag = 12

So,

Total number of marbles in a bag = 10 + 3 + 12 = 25

Now,

Probability of getting blue marble =
`(10)/(25)`

Probability of getting yellow marble =
`(3)/(25)`

Probability of getting orange marble =
`(12)/(25)`

So,

Expected value , E[x] = ∑x p(x)

= (10)(
`(10)/(25)`) + (15)(
`(3)/(25)`) + (-10)(
`(12)/(25)`)

=
`(100)/(25) + (45)/(25) - (120)/(25)`

=
`(100 + 45 - 120)/(25)`

=
`(25)/(25)`

= 1

So,

Expected value = 1

So,

The correct option is -

Yes, because the Expected value is 1 and not negative which would imply that there is a chance of winning.