Question

There is a game involving three coin tosses. Suppose you get $6 if you get three Tails but lose $2 otherwise. Would you play this game? Why or why not? Write your reason using the term "expected value."

A. Yes, the expected value is positive.
B. No, the expected value is negative.
C. Maybe, it depends on luck.
D. None

Answer 1

The game has a negative expected value of -$1, and because of this one should not play the game since, on average, it would result in a loss of money over time.

Step-by-step explanation:

The question involves the expected value calculation of a game with three coin tosses. To decide whether to play or not, one must calculate the expected monetary outcome of the game. The expected value (EV) is given by the sum of probabilities of each outcome multiplied by its corresponding value. When you win (three tails), the probability is (1/2)^3 = 1/8, and you get $6. Otherwise, the loss (not three tails) happens with probability 7/8, and you lose $2.

So, the expected value is EV = (1/8)*6 + (7/8)*(-2). When calculating, EV = 0.75 - 1.75 = -1. This means the expected value of this game is negative (-$1), and therefore on average, you will lose money each time you play. Hence, the answer is B. No, because the expected value is negative, indicating that over the long term, you should expect to come out behind in money.