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

Step-by-step explanation:

Total outcome = 52

Favorable Outcome = 8

Probability of drawing a card with a value of three or less =
`(Favorable\ outcome)/(Total\ outcome)`

=
`(8)/(52)`

=
`(2)/(13)`

Probability of drawing a card with a value of more than three = 1 -
`(2)/(13)`

=
`(11)/(13)`

Hence,

Expected value =
`146 * (2)/(13) + (-24) * (11)/(13)`

= 22.338 - 20.304

= $2.034