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−x objects of type B under the hypergeometric distribution is given by the following formula. In a lottery game, a bettor selects six numbers from 1 to 56 (without repetition), and a winning six-number combination is later randomly selected. Find the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use A=6, B=50, n=6, and x=2.)

          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−x
objects of type B under the hypergeometric distribution is given
by the following formula. In a lottery game, a bettor
selects
six
numbers from 1 to
56
(without repetition), and a winning
six-number
combination is later randomly selected. Find the probabilities
of getting exactly
two
winning numbers with one ticket. (Hint: Use
A=6,
B=50,
n=6,
and
x=2.)

Added by Austin A.

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