A deck of cards contains 52 cards, of which 4 are aces. You are offered the foll

Question

A deck of cards contains 52 cards, of which 4 are aces. You are offered the following. Draw one card at random from the deck. You win $11 if the card drawn is an ace, otherwise you lose $1. If you make this wager very many times, what will the mean outcome be A deck of cards contains 52 cards, of which 4 are aces. You are offered the following. Draw one card at random from the deck. You win $11 if the card drawn is an ace, otherwise you lose $1. If you make this wager very many times, what will the mean outcome be

Explanation / Answer

probability of drawing an ace=P(A)=number of aces/total cards=4/52=1/13

probability of not drawing an ace=P(A')=1-P(A)=1-1/13=12/13

let X is winning amount then

X=11 with P(X)=1/13

X=-1 with P(X)=12/13

E(X)=sum(X*P(X))=11*1/13 +(-1)*12/13=-1/13

so there is loss in this game with per game loss is 1/13 as E(X) is negative

if one will play 100 time then expected loss is 100/13

X 11 -1 sum P(X) 1/13 12/13 1 X*P(X) 11/13 -12/13 -1/13

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