(a) Compute the missing probability, or the probability that you match all three numbers (or "win" the lottery). (b) You pay $2 to purchase one lottery ticket. If you match zero numbers, you win nothing. If you match 1 number, you get a free lottery ticket (or win back your $2); if you match 2 numbers you win $10, if you match all three numbers you win $1000. Would you buy a lottery ticket? (Hint: Consider your profit on each outcome.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Wrap Up Exercise 1: You are faced with the following lottery: Three tickets are chosen at random (and
without replacement) from a "pool" of 25 tickets numbered #1, #2, ..., #24, #25.. After the three 'winning
numbers" are drawn, you are to count "how many" of the numbers appearing on your lottery ticket match
the numbers appearing on the winning ticket. A distribution of the probabilities associated with the random
variable x that counts the number of winning numbers you have matched on your ticket, is given below.
Values of x
P(observe x)
0
0.6697
1
0.3013
2
0.0287
3
?
(a) Compute the missing probability, or the probability that you match all three numbers (or “win” the
lottery).
(b) You pay $2 to purchase one lottery ticket. If you match zero numbers, you win nothing. If you match
1 number, you get a free lottery ticket (or win back your $2); if you match 2 numbers you win $10, if
you match all three numbers you win $1000. Would you buy a lottery ticket? (Hint: Consider your
profit on each outcome.)
Transcribed Image Text:Wrap Up Exercise 1: You are faced with the following lottery: Three tickets are chosen at random (and without replacement) from a "pool" of 25 tickets numbered #1, #2, ..., #24, #25.. After the three 'winning numbers" are drawn, you are to count "how many" of the numbers appearing on your lottery ticket match the numbers appearing on the winning ticket. A distribution of the probabilities associated with the random variable x that counts the number of winning numbers you have matched on your ticket, is given below. Values of x P(observe x) 0 0.6697 1 0.3013 2 0.0287 3 ? (a) Compute the missing probability, or the probability that you match all three numbers (or “win” the lottery). (b) You pay $2 to purchase one lottery ticket. If you match zero numbers, you win nothing. If you match 1 number, you get a free lottery ticket (or win back your $2); if you match 2 numbers you win $10, if you match all three numbers you win $1000. Would you buy a lottery ticket? (Hint: Consider your profit on each outcome.)
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