Question

A bag contains 8 green marbles, 5 yellow marbles, and 12 black marbles. If a green marble is drawn, you win $10. If a yellow marble is drawn, you win $15. If a black marble is drawn, you lose $10. It costs $1 to play. Should you play the game? Justify your answer

Answer 1

Hey hopes this helps

Explanation:

o determine whether you should play the game or not, we can calculate the expected value (EV) of playing the game. The EV represents the average outcome you can expect over the long run if you play the game many times.

The EV can be calculated as follows:

EV = (probability of winning green * amount won from green) + (probability of winning yellow * amount won from yellow) + (probability of winning black * amount lost from black) - cost to play

Probability of winning green = 8/25

Amount won from green = $10

Probability of winning yellow = 5/25

Amount won from yellow = $15

Probability of winning black = 12/25

Amount lost from black = -$10

Cost to play = -$1

Substituting the values:

EV = (8/25 * $10) + (5/25 * $15) + (12/25 * -$10) - $1

EV = $3.20 - $1

EV = $2.20

Since the EV is positive ($2.20), this means that on average, you can expect to win $2.20 per game