1. If you bet $1 in Kentucky?s Pick 4 lottery game, you either
lose $1 or gain $4999. The game is played by selecting a four-digit number between 0000 and 9999. If you $1 on 1234, what is your expected value of gain or less?
2. Let a random variable X represent the number of girls in a family of four children. Construct a table describing the probability distribution, and then find the mean and standard deviation.
3. The Medassist Pharmaceutical Company receives large shipments of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 24 tablets, then accept the whole batch if there is only one or none that doesn?t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?
4. In a test of the MicroSort method of gender selection, 51 babies are born to couples trying to have baby boys, and 39 of those babies are boys. If the gender selection method has no effect on boys and girls, find the mean and standard deviation for the number of boys born in groups of 51.
5. The author purchased a slot machine that is configured so that there is a 1 2000
probability of winning the jackpot on any individual trial. Although no one would seriously consider tricking the author, suppose that a guest claims that she played the slot machine 5 times and hit the jackpot twice.
-Find the probability of exactly two jackpots in 5 trials.
-Find the probability of at least two jackpots in 5 trials.
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