Expected value Flashcard

Front

What is expected value in probability?

Back

Expected value is the average outcome of a random event, calculated by multiplying each possible outcome by its probability and summing these products.

Front

How do you calculate expected value?

Back

Expected Value (EV) = (Probability of Outcome 1 * Value of Outcome 1) + (Probability of Outcome 2 * Value of Outcome 2) + ...

Front

What is the expected value of a life insurance policy with a premium of $235 and a payout of $250,000 with a survival probability of 0.999965?

Back

EV = (0.999965 * -235) + (0.000035 * 250000) = $226,250.

Front

In the game Deal or No Deal, how do you determine if the banker's offer is fair?

Back

Compare the banker's offer to the expected value of the remaining amounts. If the expected value is higher, the offer is not fair.

Front

What is the expected value of a fire insurance policy with a premium of $300 and a payout of $200,000 with a fire probability of 0.0002?

Back

EV = (0.9998 * -300) + (0.0002 * 200000) = $195,406.06.

Front

What does it mean if a game is 'fair'?

Back

A game is fair if the expected value of playing the game is zero, meaning neither the player nor the house has an advantage.

Front

What is the expected value of picking a paw sticker where winning (orange or blue) is worth $0.50 and losing (any other color) costs $1.00?

Back

EV = (1/3 * 0.50) + (2/3 * -1) = -$0.50.

Front

What is the probability of success for a new mousetrap if it is estimated to be 3/4?

Back

The probability of success is 0.75 or 75%.

Front

How do you calculate the expected gain or loss for a business venture?

Back

Expected Gain/Loss = (Probability of Success * Profit) - (Probability of Failure * Cost).

Front

What is the expected value of a game where you win $120,000 with a 3/4 chance and lose $98,000 with a 1/4 chance?

Back

EV = (0.75 * 120000) - (0.25 * 98000) = Gain $65,500.