On a T.v. game show a 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 behind them have $40000 foreign car, a $3 silly straw, and a $50 math textbook?
How do you start this?
To start solving this problem, we need to calculate the expected value of the selection. The expected value (EV) represents the average outcome if we repeated the experiment multiple times.
Step 1: Assign probabilities to each door
Since the contestant has an equal probability of selecting any door, we assign a probability of 1/3 to each door.
Step 2: Calculate the expected value
To find the expected value, we multiply the value of each door by its probability, and then sum up these values.
Let's proceed with the calculation:
Door 1 (Foreign car): Value = $40,000, Probability = 1/3
Door 2 (Silly straw): Value = $3, Probability = 1/3
Door 3 (Math textbook): Value = $50, Probability = 1/3
Expected Value (EV) = (Value of Door 1) * (Probability of selecting Door 1) + (Value of Door 2) * (Probability of selecting Door 2) + (Value of Door 3) * (Probability of selecting Door 3)
EV = ($40,000 * 1/3) + ($3 * 1/3) + ($50 * 1/3)
Now we can simply calculate the expected value.
EV = ($13,333.33) + ($1) + ($16.67)
EV = $13,350
Therefore, the expected value of the selection is $13,350.