If you draw a card with a value of four or less from a standard deck of cards, I will pay you $7. If not, you pay me $6. (Aces are considered the highest card in the deck.)

Question

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

You can my solution and answer here:

https://drive.google.com/file/d/1axl-k4GCSp-cmgDbUUpy8NJ8oQIkf3l0/view?usp=sharing

Answer 2

In a deck of 52 cards, considering aces have the highest value: 

1. there are 12 cards with a value 4 or less (i.e., four 2s, four 3s, and four 4s). Hence the probability that you will draw a card with a value of four or less from a deck of 52 cards is equal to 12/52
2. there are 40 cards remaining all with a value more than 4. Hence the probability that you will draw a card with a value more than 4 from a deck of 52 cards is equal to 40/52

If you draw a card with a value 4 or less, you gain $7

1. i,e, expected gain from a draw = (12/52)*52.

If you draw a card with a value more than 4, you lose $6.

1. i.e., expected loss = -(40/52)*52.

Therefore, Expected value of the proposition or E(x) = (12/52)*52 -(40/52)*52. = -$3.

In other words, you can expect to lose $3 every time you draw a card under given circumstances.