APPLICATIONS

Committee Membership A mathematics department consists of ten men and eight women. Six mathematics faculty members are to be selected at random for the curriculum committee.

(a) What is the probability that two women and four men are selected?

(b) What is the probability that two or fewer women are selected?

(c) What is the probability that more than two women are selected?

(a)

To find:

The probability that two women and four men are selected.

Given:

The mathematics department consists of ten men and eight women. Six mathematics faculty members are to be selected randomly for the committee.

Approach:

The number of combinations of selecting r objects from a total of n objects is,

C(n,r)=n!r!(n−r)!

Let S be the sample space and all outcomes are equally likely. The probability of an event E denoted by P(E) is,

P(E)=n(E)n(S)=number of favourable outcomestotal number of outcomes

Calculation:

Let E be the event where two women and four men are selected.

The selection is random, so the number of combinations of selecting 2 women from a total of 8 is C(8,2)

(b)

To find:

The probability that two or fewer women are selected.

(c)

To find:

The probability that more than two women are selected.