Hi everyone! First post here I'm going through a practice exam without solutions at the moment, and came across a statistics question I couldn't quite figure out:
3,000 numbers are drawn from a pool of 200,000 for a lottery - and each of the 3000 is drawn without replacing any, and recorded on a piece of paper. One ticket is then drawn from the pool of 200,000 after the 3,000 are returned, and if this 1 matches any of the previously drawn 3000, the prize is awarded.If no prize is won (the one drawn is not any of the initial 3000), and another is drawn. This is repeated until there is a winner.
The question has four parts, and I can't get the last part: What is the expected winning of this jackpot lottery? I believe is related to E(X) (expected values) or Expected Value of Binomial distribution. If someone could point me in the right direction, that would be greatly appreciated.
There are three sub-questions before it, which may provide some context:
What is the probability than a prize is won for any draw? 3,000/200,000
Jackpot is initially $15,000, and goes up by 15,000 each time there fails to be a winner. What is the chance that the prize will exceed winnings of $375,000? There must be no winner 25 times - and thus, there will be 26 draws. (197/200)^25 * (3/200)
Suppose X is a random variable signifying the number of draws until there is a winner. What is P (X = k)? What is the total prize money won in this instance? P(X=k) = (197/200)^ (k-1) * (3/200)
Thanks in advance!
3,000 numbers are drawn from a pool of 200,000 for a lottery - and each of the 3000 is drawn without replacing any, and recorded on a piece of paper. One ticket is then drawn from the pool of 200,000 after the 3,000 are returned, and if this 1 matches any of the previously drawn 3000, the prize is awarded.If no prize is won (the one drawn is not any of the initial 3000), and another is drawn. This is repeated until there is a winner.
The question has four parts, and I can't get the last part: What is the expected winning of this jackpot lottery? I believe is related to E(X) (expected values) or Expected Value of Binomial distribution. If someone could point me in the right direction, that would be greatly appreciated.
There are three sub-questions before it, which may provide some context:
What is the probability than a prize is won for any draw? 3,000/200,000
Jackpot is initially $15,000, and goes up by 15,000 each time there fails to be a winner. What is the chance that the prize will exceed winnings of $375,000? There must be no winner 25 times - and thus, there will be 26 draws. (197/200)^25 * (3/200)
Suppose X is a random variable signifying the number of draws until there is a winner. What is P (X = k)? What is the total prize money won in this instance? P(X=k) = (197/200)^ (k-1) * (3/200)
Thanks in advance!
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