SOLUTION: Dawn and Mike play the following game. Dawn picks a card from a deck of cards. If she selects a black king, Mike will give her $25. If not, she has to give Mike $2. Should Dawn pla

Algebra ->  Probability-and-statistics -> SOLUTION: Dawn and Mike play the following game. Dawn picks a card from a deck of cards. If she selects a black king, Mike will give her $25. If not, she has to give Mike $2. Should Dawn pla      Log On


   

Question 1117991: Dawn and Mike play the following game. Dawn picks a card from a deck of cards. If she selects a black king, Mike will give her $25. If not, she has to give Mike $2. Should Dawn play this game? What is her expected value?
P.S. - If you can answer this question, can you please explain/show me how to solve this problem using the "Expected Value" formula which is, "E = P1xA1 +P2xA2 + P3xA3"? Thanks.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
What's the probability of drawing a black king?
There are two of them in a standard deck of 52 cards so,
P%28BK%29=2%2F52=1%2F26
So the complement or the probability of not drawing a black king is,
P%28NBK%29=1-1%2F26=25%2F26
Her expected earnings would then be,
E=%281%2F26%29%2825%29-%2825%2F26%29%282%29
E=25%2F26-2%2825%2F26%29
E=-25%2F26
So she should expect to lose about 96 cents each time she plays.
She probably shouldn't play this game unless she likes to lose.