Question 1086242: A local lottery is selling scratch-off tickets for $3.00 each. There are nine scratch-off spots consisting of the following dollar amounts: Four $5 spots, three $10 spots, and two $20 spots. If you scratch only two and get a matching pair you win the dollar amount listed ($5, $10, or $20).
a. What is the probability that you will NOT win any prize?
b. What is the probability that you will win $20?
c. Find your expected gain or loss.
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:A local lottery is selling scratch-off tickets for $3.00 each. There are nine scratch-off spots consisting of the following dollar amounts: Four $5 spots, three $10 spots, and two $20 spots. If you scratch only two and get a matching pair you win the dollar amount listed ($5, $10, or $20).
a. What is the probability that you will NOT win any prize?
b. What is the probability that you will win $20?
c. Find your expected gain or loss.
Solution:
Expected value is calculated by summing, for all possible outcomes,
∑pi(Xi)
where
pi = probability of outcome i
Xi = revenue (gain-cost) of outcome i.
For the given scratch-off sale, customers pay $3 whether they win or not.
The spots are:
$5 (4)
$10 (3)
$20 (2)
By scratching 2 and match, customer get the amount (less $3 already paid).
P($5)=4/9*3/8=1/6
P($10)=3/9*2/8=1/12
P(20)=2/9*1/8=1/36
(a) probability of winning nothing (i.e. lose $3)
P(0)=1-(1/6+1/12+1/36)=1-5/18=13/18
(b)P($20)=1/36 (see above)
(c) E[X]
=(5-3)P($5)+(10-3)P($10)+(20-3)P($20)+(0-3)P(0)
=2(1/6)+7(1/12)+17(1/36)+(-3)(13/18)
= -7/9 =-0.78 (approx.)
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