Question

A dart lands randomly on a board with colored sectors: 7 sectors colored red, 6 sectors colored blue and 8 sectors colored black. If your dart lands on a red sector, you win $5, if it lands on a black sector, you win $10, if it lands on a blue sector you lose $8. What is the expected value if you play this game?

Answer 1

The expected value of playing this game is -$1.57. Based on the expected value, it is not advisable to play this game with the intention of winning money.

Step-by-step explanation:

The expected value of playing this game can be calculated by multiplying the probability of each outcome by the corresponding amount you win or lose. Let's calculate the expected value step by step:

1. Probability of landing on a red sector = 7/21
2. Probability of landing on a blue sector = 6/21
3. Probability of landing on a black sector = 8/21
4. Expected value = (Probability of red sector * $5) + (Probability of blue sector * -$8) + (Probability of black sector * $10)
5. Expected value = (7/21 * $5) + (6/21 * -$8) + (8/21 * $10)
6. Expected value = $35/21 - $48/21 + $80/21
7. Expected value = ($35 - $48 + $80)/21
8. Expected value = -$33/21
9. Expected value = -$1.57

The expected value, rounded to the nearest cent, is -$1.57. This means that if you play this game repeatedly over a long period of time, you can expect to lose an average of $1.57 per game. Based on the expected value, it is not advisable to play this game with the intention of winning money.