Question

7. Alicia is playing a game by drawing a card from a standard deck and replacing it. If the card is an Ace card, Alicia win $100. If it is not an Ace card, she pay $10. There are 4 Ace cards in a deck of 52 cards.

Should Alicia play the game?

A. Yes, she is expected to win money in the long term.

B . No, she is expected to lose money in the long term.

Answer 1

let X be the outcome of the game

P(X=100) =P(getting an ace) =4/52
P(X=-10) =P(not getting an ace) =48/52

expected value of the game E(x) =xP(x) =100*4/52-10*48/52 = -1.54

since expected value is negative:

B . No, she is expected to lose money in the long term