SOLUTION: Pick a card: Mike and Dave play the following game. Mike picks a card from a deck of cards. If he selects a heart, Dave gives him $5. If not, he gives Dave $2. a) Determine Mike

Click here to see ALL problems on Probability-and-statistics

Question 283185: Pick a card: Mike and Dave play the following game. Mike picks a card from a deck of cards. If he selects a heart, Dave gives him $5. If not, he gives Dave $2.
a) Determine Mike�s expectation
b) Determine Dave�s expectation.
I am completely lost. I know there are 52 cards in a deck and I know that of that, 13 are hearts. But I am lost as to where to go after that.
Thanks for any help!
Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!
Pick a card: Mike and Dave play the following game. Mike picks a card from a deck of cards. If he selects a heart, Dave gives him $5. If not, he gives Dave $2.

Mike's net winnings are +$5 if he selects a heart or -$2 if he doesn't select a heart Mike's expectation = (net winnings if he gets a heart)*(probability of getting a heart) plus (net winnings if he doesn't get a heart)*(prob of not getting a heart) Probability of Mike getting a heart = or Probability of Mike NOT getting a heart = or So, Mike's expectation = If they continue to play the game many times, in the end Mike will have averaged LOSING 25 cents per game. ---------------------------- Dave's net winnings are -$5 if Mike selects a heart or +$2 if he doesn't select a heart Dave's expectation = (net winnings if Mike gets a heart)*(probability of Mike getting a heart) plus (net winnings if Mike doesn't get a heart)*(prob of Mike not getting a heart) Probability of Mike getting a heart = or Probability of Mike NOT getting a heart = or So, Dave's expectation = If they continue to play the game many times, in the end Dave will have averaged WINNING 25 cents per game. Edwin