Question

You are playing a game where you are rolling a fair 6-sided number cube. It costs $1.00 for every roll. If you roll an even number, you win $3.00. If you roll an odd number, you win nothing. Which of the following is the expected value of this game?

a) expected value= $-0.50

b) expected value= $0.50

c) expected value= $1.00

d) expected value= $-1.00

Answer 1

The expected value of the game with a fair 6-sided die where even rolls win $3 and odd rolls win nothing, after taking into account the cost of $1 per roll, is $0.50.

Step-by-step explanation:

To calculate the expected value of the game, we have to consider the possible outcomes and their associated probabilities and payouts. Since a fair 6-sided die has an equal chance of rolling any number from 1 to 6, the probability of rolling an even number (2, 4, or 6) is ½, and the probability of rolling an odd number (1, 3, or 5) is also ½.

When you roll an even number, you win $3.00 but have paid $1.00 to play, resulting in a net gain of $2.00. When you roll an odd number, you win nothing but have paid $1.00 to play, resulting in a net loss of $1.00.

Now, we can calculate the expected net gain per roll like so:

Winning situation (even roll): (½) * ($2.00)

Losing situation (odd roll): (½) * (-$1.00)

The expected value (υ) is the sum of these situations:

υ = (½ * $2.00) + (½ * -$1.00) = $1.00 - $0.50 = $0.50

Therefore, the correct answer is b) expected value= $0.50.

Answer 2

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