A state runs a lottery in which 6 integer numbers are randomly selected from [0,

Question

A state runs a lottery in which 6 integer numbers are randomly selected from [0, 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 4 of the 6 numbers chosen by a player appear in the state’s sample? c) If a player enters one lottery each week, what is the expected number of weeks until the player matches all 6 numbers in the state’s sample?

Explanation / Answer

The number of ways selecting 6 number from 0 to 39 numbers without replacement is 40C6 = 3838380

a) The probability that the 6 numbers chosen by a player match all 6 numbers in the state’s sample is 1 / 40C6 = 0.00000026

b) The probability that 4 of the 6 numbers chosen by a player appear in the state’s sample is 6C4 * 36C2 / 40C6 = (15*630) / 3838380 = 0.002462

c) 1/0.00000026 = 3838380 weeks = 71081.111 years

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