Question

You roll a six sided die. You are given $8 if a 6 comes up, $2 if a 3, 4, 5 comes up, and

Answer 1

We want to get the expected value for the given experiment. We will see that the expected value is $2.33

For an experiment with outcomes {x₁, ..., xₙ} each one with probability {p₁, ..., pₙ} the expected value is defined as:

EV = x₁*p₁ + ... + xₙ*pₙ

Here we have 3 outcomes:

• x₁ = winning $8
• x₂ = winning $2
• x₃ = winning $0.

For x₁ we need to roll a 6, this is a probability of 1 out of 6, then:

p₁ = 1/6

For x₂ we need to roll a 3, 4, or 5 (3 out of 6), then:

p₂ = 3/6

For x₃ we need to roll a 1 or a 2 (2 out of 6) so the probability is:

p₃ = 2/6

Then the expected value is:

EV = $8*(1/6) + $2*(3/6) + $0*(2/6) = $2.33

If you want to learn more about expected values, you can read:

brainly.com/question/15858152