Friday

January 30, 2015

January 30, 2015

Posted by **James** on Monday, February 23, 2009 at 11:07pm.

If a group of 5 applicants (consisting of 2 women and 3 men) apply for a license, what is the probability that...

a) Exactly 2 of the 5 applicants take the same test?

b) The 2 women take the same test?

- College Level Probability -
**Count Iblis**, Tuesday, February 24, 2009 at 8:25amCount the number of ways you can assign test to the people and then divide by the total number of ways (which is 4^5).

There are 4 ways to choose which test is going to be done by two given applicants who take the same test. There are Binomial[5,2] ways to choose these two applicants.

The remaining 3 applicants must be assigned any one of the 3 other tests. There are 3^3 ways for this.

Now,

4*Binomial[5,2]*3^3

is not the correct answer, because of the double counting of the cases where 2 out of 3 of the remaining group of 3 are also assigned the same test.

Depending on how the question is to be interpreted, such cases should not be counted at all, or they should be counteed once. So, you need to compute the number of these cases and then subtract that once or twice from the above expression.

You can also try a more formal approach using the principle of inclusion and exclusion.

- College Level Probability -
**Anonymous**, Thursday, November 20, 2014 at 12:51pma 15/256, b 1/6

**Answer this Question**

**Related Questions**

Math/probability - Five different written driving tests are administered by the ...

hard probability question - four different written driving tests are ...

MATH/Probability - our different written driving tests are administered by the ...

college - Four hundred people apply for three jobs. 130 of the applicants are ...

Algebra - A student is taking a literature course in which four tests are given...

math - jones attained the following scores in three tests 36,75,60. if his ...

Error ! question - If the company administers n=10 identical triangle taste ...

Maths - Jim has grades of 84, 65, and 76 on three math tests. What grade must he...

math - jim has grades of 84, 65, 76 on three tests. what grade must he obtain on...

math - Jennifer's scores on her first four science tests were 85, 76, 89 and 92...