# MATH 157

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On a TV game show, the contestant is asked to select a
door and then is rewarded with the prize behind the door
selected. If the doors can be selected with equal probability,
what is the expected value of the selection if the
three doors have behind them a \$40,000 foreign car, a \$3
silly straw, and a \$50 mathematics textbook?

• MATH 157 -

Each door has a prob of 1/3

expected value
= 1/3( 40000 + 3 + 50 ) = 13351

• MATH 157 -

How did you get this answer I want to make sure im doing this correctly, thank you.

• MATH 157 -

expected return on picking first door
= (1/3)(4000)
expected return on second door
= (1/3)(3)
expected return on third door
= (1/3)50)

so expected return on whole event
= (1/3)(4000) + (1/3)(3) + (1/3)(50)
= (1/3)( 40000 + 3 + 50 ) = 13351 as above

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