Question

If you draw a card with a value of two or less from a standard deck of cards, I will pay you $30

. If not, you pay me $6
. (Aces are considered the highest card in the deck.)

Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

Answer and Step-by-step explanation:

The expected value of a proposition is the sum of all possible outcomes, each multiplied by its probability. In this case, there are two possible outcomes: drawing a card with a value of two or less, and drawing a card with a value higher than two.

In a standard deck of cards, there are four cards with a value of two (one of each suit) and four cards with a value of one (one of each suit). So, the probability of drawing a card with a value of two or less is 8/52 or 2/13.

The expected value of the proposition is therefore:

(2/13) * $30 + (11/13) * (-$6) = $-0.92

So, the expected value of the proposition is approximately $-0.92, rounded to two decimal places.