1. (10 points total) Suppose you play a card game at a carnival. It costs 2 doll
ID: 3369078 • Letter: 1
Question
1. (10 points total) Suppose you play a card game at a carnival. It costs 2 dollars to play the game. The dealer randomly shuffles 4 cards. Only one of the 4 cards is an Ace. You get to choose a single card. If it is the Ace, you win 10 dollars. (a) (5 points) What is your expected (mean) winnings playing this game? (keep in mind you paid 2 dollars to play the game) (b) (5 points) Suppose after you choose your card, the dealer offers to reveal one of the 3 cards you did not choose. The card he reveals is always not an Ace. For an extra1 dollar, he offers you the chance to swap your card with one of the two cards that have not yet been revealed. If you take him up on his offer, what is your expected (mean) winnings playing this game? (keep in mind you have now paid 3 dollars to play the game)Explanation / Answer
1(a)
Cost of playing game is $2 so we will reduce that from our expected (mean) winning amount.
Only 4 cards are being shuffled and we know that there is one ace out of the 4 cards which gets us winning $10.
So probably of winning $10 (in other words, probablity of getting an ace) = 1/4=.25
and probablity of not gettting an ace (i.e. not winning or winning $0) = 3/4 =.75
So expected winnings = .25*10+.75*0=2.5
Adjusting for the initial amount paid to play the game, Expected winning=2.5-2=$0.5 which is the answer
1(b) is a seperate question to be asked seperately. That will be solved using Bayes theorem (conditional probablity).
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