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Q. 2 A charity prints scratch cards each of which contain 3 squares. Each square may contain a star or an X and the printing process independently decides which symbol will be on each square such that the probability of a star is 20%. When someone buys a card they scratch the three boxes to reveal a star or an X in each box. The amount that is paid out to the player depends on the total number of stars uncovered on the card as follows Number of stars | 0 | 1 | 2 | 3 Prize Amount | $0 | $2 | $5 | $20 a) Let X be the amount paid out for a random ticket. Find the probability mass function of X. b) If it costs 5 cents to print each ticket and tickets sell for $2, what is the expected amount of profit that the charity will make on each ticket? c) What is the expected number of tickets I need to buy if I keep buying tickets until one of the tickets wins $20?

          Q. 2 A charity prints scratch cards each of which contain 3 squares. Each square may contain a star or an X and the printing process independently decides which symbol will be on each square such that the probability of a star is 20%. When someone buys a card they scratch the three boxes to reveal a star or an X in each box. The amount that is paid out to the player depends on the total number of stars uncovered on the card as follows
Number of stars | 0 | 1 | 2 | 3
Prize Amount | $0 | $2 | $5 | $20
a) Let X be the amount paid out for a random ticket. Find the probability mass function of X.
b) If it costs 5 cents to print each ticket and tickets sell for $2, what is the expected amount of profit that the charity will make on each ticket?
c) What is the expected number of tickets I need to buy if I keep buying tickets until one of the tickets wins $20?

q 2 a charity prints scratch cards each of which contain 3 squares each square may contain a star or an x and the printing process independently decides which symbol will be on each square s 98957

Added by Melanie A.

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