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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.

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1 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.

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