Question

if you draw a card with a value of 7 or less from a standard deck of cards, I will pay you $12. If not ,you pay me $13. (Aces are considered the highest card in the deck).find the expected value of the proposition. round the answer to 2 decimal places. Losses must be expressed as negative values .

Answer 1

if you draw a card with a value of 7 or less from a standard deck of cards, I will pay you $12. If not ,you pay me $13. (Aces are considered the highest card in the deck).



find the expected value of the proposition. round the answer to 2 decimal places. Losses must be expressed as negative values

Remember that

The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).

we have that

In a standard deck of cards

cards with a value of 7 or less are

2,3,4,5,6,7--------> total =6*4=24 cards

Probability that draw a card with a value of 7 or less is

P=24/52=0.4615

expected value=(0.4615)*$12-(1-0.4615)*$13

expected value=$-1.46 -----> is a loss