Question

Throw two dice. If the sum of the two dice is 7 or more, you win...

Throw two dice. If the sum of the two dice is 7 or more, you win $15. If not, you pay me $17.

Step 1 of 2 :  

Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Math   Statistics-And-Probability   
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Answer #1

A pair of dice is rolled; let X be the sum of the two numbers that appear

outcome X P(X)
(1,1) 2 1/36
(1,2)(2,1) 3 2/36
(1,3)(3,1)(2,2) 4 3/36
(1,4)(4,1)(2,3)(3,2) 5 4/36
(1,5)(5,1)(2,4)(4,2)(3,3) 6 5/36
(1,6)(6,1)(2,5)(5,2)(3,4)(4,3) 7 6/36
(2,6)(6,2)(3,5)(5,3),(4,4) 8 5/36
(3,6)(6,3)(4,5)(5,4) 9 4/36
(4,6)(6,4)(5,5) 10 3/36
(5,6)(6,5) 11 2/36
(6,6) 12 1/36

P(sum 7 or more)=21/36

===============

X P(X) X*P(X)
15 21/36 8.7500
-17 15/36 -7.0833

expected value of the proposition=mean = E[X] = Σx*P(X) = $ 1.67

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