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?
To find the expected value of the selection, we need to multiply the value of each prize by the probability of selecting that prize and then sum up the results.
Let's assign probabilities to each door:
Door 1: Probability = 1/3
Door 2: Probability = 1/3
Door 3: Probability = 1/3
Now, let's assign values to each prize:
Car: Value = $40,000
Silly Straw: Value = $3
Mathematics textbook: Value = $50
To calculate the expected value, we multiply the value of each prize by its corresponding probability and sum them up:
Expected Value = (Probability of door 1 * Value of car) + (Probability of door 2 * Value of silly straw) + (Probability of door 3 * Value of mathematics textbook)
Expected Value = (1/3 * $40,000) + (1/3 * $3) + (1/3 * $50)
Expected Value = ($13,333.33) + ($1) + ($16.67)
Expected Value = $13,350
Therefore, the expected value of the selection is $13,350.