Question

consider the following gamble: you are asked to roll a standard six-sided die. you will be paid $2 if the die shows an even number, and $1 if the die shows an odd number. what is the expected value of this gamble?

Answer 1

The expected value of the gamble is $2.00.

Step-by-step explanation:

The expected value of a gamble is calculated by multiplying each potential outcome by its probability and summing them up.

In this case, let's consider the possible outcomes:

• Rolling an even number (2, 4, or 6) with a probability of 3/6 (since there are 3 even numbers out of 6 total numbers)
• Rolling an odd number (1, 3, or 5) with a probability of 3/6 (since there are 3 odd numbers out of 6 total numbers)

For the even numbers, the payoff is $2, and for the odd numbers, the payoff is $1.

So, the expected value of the gamble is calculated as:

(3/6 * $2) + (3/6 * $1) = $1.50 + $0.50 = $2.00

Therefore, the expected value of this gamble is $2.00.