Suppose that a lottery ticket has probability p of being a winning ticket, independently of other tickets. A gambler buys 3 tickets, hoping this will triple the chance of having at least one winning...

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Suppose that a lottery ticket has probability p of being a winning ticket, independently of other tickets. A gambler buys 3 tickets, hoping this will triple the chance of having at least one winning ticket.
(a) What is the distribution of how many of the 3 tickets are winning tickets?
(b) Show that the probability that at least 1 of the 3 tickets is winning is 3p-3p2+p3, in two di?erent ways: by using inclusion-exclusion, and by taking the complement of the desired event and then using the PMF of a certain named distribution.

Answered Same DayDec 26, 2021

Answer To: Suppose that a lottery ticket has probability p of being a winning ticket, independently of other...

Robert answered on Dec 26 2021
116 Votes
1
Solution
a) The distribution of the 3 tickets would be the winning tickets is computed below:
Let assume the number of winning tickets is X. Further, X is the random variable. Where,
each ticket is considered to be the independent Bernouli trial. The probability of the success
in this...
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