Question

Suppose that you are offered the following "deal." You roll a six-sided die. If you roll a 6, you win $10. If you roll a 4 or 5, you win $1. Otherwise, you pay $5.

a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate.

Probability Distribution Table
X P(X)
-5 ?
1 ?
10 ?
b. Find the expected profit.

Answer 1

Prob(a 6) = 1/6
expected return on this roll = (1/6)($10) = $ 5/3
prob(4or5) = 1/3
expected return on this roll = $1(1/3) = $ 1/3
prob(remaining outcomes) = 3/6 = 1/2
expected return of this outcome = -5(1/2) = -$ 5/2

expected profit or loss = $( 5/3 + 1/3 - 5/2)
= - $ 1/2

Place my results in the appropriate parts of your table

I wouldn't play this game.