Question

In a game, you toss a fair coin and a fair six-sided die. If you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. Otherwise, you lose $6. What is the expected profit of one round of this game?

Answer 1

Using probabilities, it is found that the expected profit of one round of this game is of $0.

A probability is the number of desired outcomes divided by the number of total outcomes.

• One of the two sides of the coin are heads.
• 2 of the 6 sides of the dice are 3 or 6.

Hence, since the coin and the dice are independent, the probability of winning is:

$p = \frac{1}{2} \times \frac{2}{6} = \frac{1}{6}$

The expected value is the sum of each outcome multiplied by its respective probability.

In this problem:

• $\frac{1}{6}$ probability of earning $30.
• $\frac{5}{6}$ probability of losing $6.

Then:

$E(X) = 30\frac{1}{6} - 6\frac{5}{6} = 5 - 5 = 0$

The expected profit of one round of this game is of $0.

A similar problem is given at brainly.com/question/24855677