Question

random variables, probability distributions and expected value Darryl plays a card game with his sister. He uses a 52 card deck and she chooses 1 card. If she chooses the 4 of hearts, she will win $10 and if she chooses any spade, she loses $2. If any other card is drawn, they break even. What is the expected value for Darryl's sister? Round to the nearest cent. Do not round until your final calculation. Note: within a deck of cards, there are 4 equal suits: hearts, clubs, diamonds, and spades.

Answer 1

The expected value for Darryl's sister is -31 cents

Here, we want to calculate the expected value for Darryl's sister

Firstly, we shall need the probabilities of each event

In a standard deck of cards, there are 52 cards;

Out of these 52, only 1 is the 4 of hearts

The probability of selecting a 4 of the heart suite = 1/52

Probability of selecting a spade

In the suite of spades, there are 13 cards

So the probability of selecting a spade card will be 13/52 = 1/4

Drawing any other card does not add nor subtract any value from both players

So for Darryl's sister;

The expected value will be;

(1/52)($10) - 1/4($2) + 0

= 10/52 - 1/2 = (10-26)/52 = -16/52 = -$0.3077

To the nearest cent, this is 31 cents