Question

In: Math

At a charity event, a player rolls a pair of dice. If the player roles a...

At a charity event, a player rolls a pair of dice. If the player roles a pair (same number on each die), the player wins $10. If the two are exactly one number a part (like a five and a six), the player wins $6. IF the player roles a one and a six, they win $15. Otherwise, they lose. If it cost $5 to play, find the expected value. Write a complete sentence to explain what your answer means without words "Expected value". Show all work for full credit including the probability distribution.

Solutions

Expert Solution

Pay: $5 to play

X = the number of dollars won or lost.

List the values that X may take on is X ∈ {10, 6, 15,0}

Construct a PDF

P(X = 10) = 6/36 = 1/6 (There are 6 different ways in which player can roll same number on each die. Total number of combinations possible is 6*6 = 36)

P(X = 6) = 10/36 = 5/18 (There are 10 different ways in which player can roll die such that two are exactly one number apart. Total number of combinations possible is 6*6 = 36)

P(X = 15) = 2/36 = 1/18 (There are 2 different ways in which player can roll a one and a six. Total number of combinations possible is 6*6 = 36)

P(X = 0) = 18/36 = 1/2 (There are 18 different ways in which player can lose)

Expected Value = 10*1/6 + 6*5/18 + 15*1/18 + 0*1/2 - 5

Expected Value = -0.8333

Because the expected value is a negative answer, we'd say that the game is NOT fair. In the long run, players of this game will lose money.

milcah answered 1 year ago
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