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

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(20059) (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

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