If we sample from a small finite population withoutreplacement, 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 twotypes, we can use the hypergeometric distribution. If a population has A objects of onetype, while the remaining B objects are of the othertype, and if n objects are sampled withoutreplacement, then the probability of getting x objects of type A and nx objects of type B under the hypergeometric distribution is given by the following formula. In a lotterygame, a bettor selects four numbers from 1 to 48 (without repetition), and a winning four-number combination is later randomly selected. Find the probabilities of getting exactly two winning numbers with one ticket.(Hint: Use A=4, B=44, n=4, and x=2.)

P(x)=A!(Ax)!x!B!(Bn+x)!(nx)!(A+B)!(A+Bn)!n!

P(2)=?

(Round to four decimal places asneeded.)