Andy is always looking to make money fast. Lately, he has been trying to make mo
ID: 3239316 • Letter: A
Question
Andy is always looking to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen, or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs.
(a) Creat a probability model and find Andy's expected profit per game.
(b) Would you recommend this game to Andy as a good way to make money? Explain.
Explanation / Answer
Given
cost of game =$2
win =0 if number card drawn
win=$3 face card
win=$5 ace
extra win =$20 ace of club
so there total 52 cards out of which 36 number cards and 12 face cards ,4 ace cards which contains 1 ace of club
so
a)
let X is amount win and P(X=x) is probability
X P(X=x)
0 (36/52) =0.6923
3 (12/52)=0.2308
5 (3/52)=0.577
25 (1/52)=0.0192
now
Total expected amount win=E(X)=sum of x*P(X=x)
=0*0.6923+3*0.2308+5*0.0577+25*0.0192
=1.4609
so expected profit =expected win -cost
=1.4609-2=$(-0.5391)
b)
i would not recommend this game to andy as a good way to make money because there is very less chance of winning also as we calculated in part (a) expected profit is -ve so i would not recommend it.