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A state runs a lottery in which 6 numbers are randomly selected from 39, without replacement. A player chooses 6 numbers before the state's sample is selected.
(a) What is the probability that the 6 numbers chosen by a player match all 6 numbers in the state's sample?
(b) What is the probability that 5 of the 6 numbers chosen by a player appear in the state's sample?
(c) What is the probability that 4 of the 6 numbers chosen by a player appear in the state's sample?
(d) If a player enters one lottery each week, what is the expected number of weeks until a player matches all 6 numbers in the state's sample?
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What method has been used to transform Model 1 to Model 2? Equations for Model 1 and Model 2 are as follows:
Comparing the results from (a) and (e), what happens to the required sample size when we increase the confidence level?
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