Question

For this problem, assume that the committee contains 9 men and 5 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?

Answer #1

**Solution:**

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Rework problem 24 from section 3.2 of your text, involving the
subcommittee. For this problem, assume that the committee contains
6 men and 8 women and that three are selected at random for a
subcommittee. What is the probability that the subcommittee
consists of 2 men and 1 woman, given that it contains both men and
women?

A subcommittee is randomly selected from a committee of eight
men and seven women. What is the probability that all three people
on the subcommittee are men?

A committee of 5 persons is to be selected out of 6 men and 2
women. Find the number of ways in which more men are selected than
women? b) If 5 students are to be randomly chosen from a group of
12 students to form a committee for a class trip, what is the
probability that group members Alice and Tom will be chosen for the
committee?

10 men and 5 women are meeting in a conference room. Four people
are chosen at random from the 15 to form a committee.
a) What is the probability that the committee consists of 2 men
and 2 women?
b) Among the 15 is a couple, Bob and Jane. What is the
probability that Bob and Jane both end up on the committee?
c) What is the probability that Bob ends up on the committee but
Jane does not?

Rework problem 23 from section 2.4 of your text involving
congressional committees. Assume that the committee consists of 6
Republicans and 5 Democrats. A subcommittee of 4 is randomly
selected from all subcommittees of 4 which contain at least 1
Democrat. What is the probability that the new subcommittee will
contain at least 2 Democrats?

There are 7 women and 5 men in a department. (a) How many ways
can a committee of 4 people be selected if there must be 2 men and
2 women on the committee? (b) If a committee is formed at random,
what is the probability that it is made up of 2 men and 2
women.

4 people are to be chosen from 10 men and 12 women to form a
committee which contains at least two women. How many different
ways can the committee be formed? If, among the 10 men and 12
women, Mr. and Mrs. Smith can not both be selected, then how many
different ways can the committee be formed?

1.a) Nine men and two women are semifinalists in a lottery. From
this group, seven finalists are to be selected by a drawing. What
is the probability that all seven finalists will be men? (Enter
your probability as a fraction.)
b) retailer purchases 240 of a new brand of DVD player, of which
4 are defective. The purchase agreement says that if he tests 5
chosen at random and finds 1 or more defective, he receives all the
DVD players...

Assume that the committee consists of 7 Republicans and 7
Democrats. A subcommittee consisting of 5 people is to be
selected.
1) How many such subcommittees are possible if each subcommittee
must contain exactly 3 Republicans and 2 Democrats?
2) How many such subcommittees are possible if each subcommittee
must contain at least 1 and no more than 2 Democrats?

A committee of 5 will be chosen from a group of 4 men and 6
women. What is the probability that at least 3 men are chosen?

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