Question

find the expected value of the proposition.round your answer to two decimal places. losses must be expressed as negative values.

Answer 1

To find the expected value of the question, we need to find the probability of having a card with a value less or equal to 5, and the probabilities greater than 5. We are told that the aces are considered the highest card in the deck. So, this card is not part of the group less or equal to 5.

Then, we have in a standard deck of cards 52 cards.

• Those cards that are equal or less than 5 are 16 cards.

,

• Those cards that are greater than 5 are 36 cards.

The probability of having a card equal to or less than 5 is equal to:

`P(C\leq5)=(16)/(52)`

The probability of having a card greater than 5 is equal to:

`P(C>5)=(36)/(52)`

When we pay someone, we have a "loss" in a game. Then, if we pay $22, we need to write this value as -$22.

Therefore, the expected value of the proposition is as follows:

`E(V)=(16)/(52)\cdot39-(36)/(52)\cdot22=-3.23076923077`

If we round the result to two decimal places, we have that the expected value is equal to E(V) = $ -3.23.