Question

You are presented with a deck of 20 cards, numbered from 1 to 20 and can draw one card. If the number is odd, you win $13. If the number is even, you win nothing. If you play the game, what is the expected payoff? $

Answer 1

Explanation:

To calculate the expected payoff, we need to multiply the amount won by the probability of winning, and then add up all the results.

There are 10 odd numbers and 10 even numbers in the deck, so the probability of drawing an odd number is 10/20 = 1/2, and the probability of drawing an even number is also 1/2.

If we draw an odd number, we win $13, and if we draw an even number, we win $0. Therefore, the expected payoff is:

(1/2) × $13 + (1/2) × $0 = $6.50

So on average, we can expect to win $6.50 per game if we play this game many times.