If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type A and
nminus−x
objects of type B under the hypergeometric distribution is given by the following formula. In a lottery game, a bettor selects
sixsix
numbers from 1 to
4646
(without repetition), and a winning
sixsix-number
combination is later randomly selected. Find the probabilities of getting exactly
threethree
winning numbers with one ticket. (Hint: Use
Aequals=66,
Bequals=4040,
nequals=66,
and
xequals=33.)
P(x)equals=StartFraction A exclamation mark Over left parenthesis Upper A minus x right parenthesis exclamation mark x exclamation mark EndFraction times StartFraction B exclamation mark Over left parenthesis Upper B minus n plus x right parenthesis exclamation mark left parenthesis n minus x right parenthesis exclamation mark EndFraction divided by StartFraction left parenthesis Upper A plus Upper B right parenthesis exclamation mark Over left parenthesis Upper A plus Upper B minus n right parenthesis exclamation mark n exclamation mark EndFractionA!(A−x)!x!•B!(B−n+x)!(n−x)!÷(A+B)!(A+B−n)!n!
Question content area bottom
Part 1
P(33)equals=enter your response here
(Round to four decimal places as needed.)