Question

1. A state runs a lottery in which five numbers are randomly selected from 45 numbers without replacement. A player chooses five numbers before the state's sample is selected.
a. what is the probability that the five numbers chosen by a player match all five numbers in the state's sample?
b. If a player enters one lottery each week, what is the expected number of weeks until a player matches all five numbers in the state's sample (caution: to get the full credit you need to fully justify your answer by clearly stating the name of used probability distribution?)

Answer 1

a)

probability that the five numbers chosen by a player match all five numbers in the state's sample

=P(select 5 out of 5 winning and none from rst of 45 )=(₅C₅)*(₄₀C₀)/(₄₅C₅) =1*1/1221759 =1/1221759

b)here this folllows geometric distribution with parameter p=1/1221759

expected number of weeks until a player matches all five numbers in the state's sample E(x) =1/p=1221759