Expected returns: John is watching an old game show rerun on television called L

Question

Expected returns: John is watching an old game show rerun on television called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $150, and behind the other is a round-the world trip worth $7,200. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection, and what is the standard deviation of that selection?

Explanation / Answer

1)

Expected Cost = probability * cost

Expected Cost = 150*75%+7200*25%

                           = 112.5 + 1800

                           = 1912.50

Expected Cost of the Gift would be $ 1912.50

2)

standard deviation = sqrt( summation of (probability * ( value- expected value)^2 )

standard dev = sqrt( 0.75 * ( 150 - 1912.50) ^2 + 0.25 * ( 1800 - 2368.75) ^2) = 1527.40

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