Question

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $208. If not, you pay me $35. (Aces are considered the highest card in the deck.) Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

The expected value of the proposition which is the net expected outcome is; $20.89.

How to find the expected value?

We are given that;

There is a deck of cards.

There are 3 kinds of cards that have value under 4 (or equal). These 3 cards are 2, 3, 4 and they are in total 4 * 3 = 12 cards.

The probability that we draw such a card = 12/52 = 0.23.

Thus, the probability that we do not draw such a card = 1 - 0.23 = 0.77.

Now, If we play the game once, we will get 0.23 of the times $208 and 0.77 of the times $35.

Thus, the net total expected outcome is: (0.23*208) - (0.77*35)

= $20.89.

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