Question

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $146. If not, you pay me $24. (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: Expected value = $2.034

Explanation:

Total outcome = 52

Favorable Outcome = 8

Probability of drawing a card with a value of three or less = $\frac{Favorable\ outcome}{Total\ outcome}$

= $\frac{8}{52}$

=  $\frac{2}{13}$

Probability of drawing a card with a value of more than three = 1 -  $\frac{2}{13}$

=  $\frac{11}{13}$

Hence,

Expected value = $146 \times \frac{2}{13} + (-24) \times \frac{11}{13}$

= 22.338 - 20.304

= $2.034