Question

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

n minus−x objects of type B under the hypergeometric distribution is given by the following formula. In a lottery​ game, a bettor selects

five numbers from 1 to55​(without repetition), and a winning five​-number combination is later randomly selected. Find the probabilities of getting exactly three winning numbers with one ticket.​ (Hint: Use A equals=5,B equals=50,n equals=5​,and

x equals=3​.)

​P(x)equals=A!/(A−x)!x!•B!/(B−n+x)!(n−x)!÷(A+B)!/(A+B−n)!n!

​P(3​)equals=

​(Round to four decimal places as​ needed.)

Answer 1