A 3-person committee is to be formed by selecting from a group of 5 men and six women, one of whom is Jane. What is the probability of selecting a committee with 1 man and 2 women, one of whom must be Jane?
Please show your work on you arrived at this one. I've asked the question before; but I'm a rookie and need help with the nomenclature. I need to understand the logic behind the answer so I can transfer the knowledge to another application.
Eric S
Favorite Answer
There are 11 C 3 ways to choose the committee, or
(11!)/(8!*3!) = 165
There are 5 ways to select the one man for the desired committee, 1 way to select Jane, and 5 ways to select the other woman.
5*1*5 = 25 different committees which meet the criteria.
So the probability of choosing that particular committee, assuming it's random, is
25/165 = 5/33
alwbsok
To calculate the probability, you need to count the number of desirable outcomes (i.e. the number of ways to select a 1 man, 1 woman, and 1 Jane committee) and divide that by the total number of outcomes (i.e. the number of 3 person committees that can be made from Jane and 2 other people).
First we'll count the number of committees that are desirable. We need one man (we have 5 choices), one Jane (one choice), and one other woman (5 choices). So the total number will be:
5 * 1 * 5 = 25
Now we count the total number of possible committees. We have one choice for the Jane, and 10 other people to choose 2 people from. The number will be:
1 * (10 C 2)
Where 10 C 2 is the number of unordered selections of 2 objects from 10 objects. Many scientific calculators can calculate selections like this, and it comes to 45. So the probability will be:
P = 25/45 = 5/9
maxine t
Note: The degree of the quotient is one less than the degree of the dividend. And the degree of the remainder is less than the degree of the divisor, x + 3, which in this case is 1. The remainder therefore is of degree 0, which is a number.
In general, if we divide a polynomial of degree n by a polynomial of degree 1, then the degree of the quotient will be n â 1. And the remainder will be a number.
Mugen is Strong
P(Jane, a woman and a man)
= 1C1 * 5C1 * 5C1 / 11C3
= 1*5*5 / 165
= 5 / 33