A committee of 2 women and 6 men is to be chosen randomly from a group...

A committee of 2 women and 6 men is to be chosen randomly from a group of 18 women and 13 men.

a) What is the probability that "Ann" (female) and her friend "Bob" (male) are on the committee together?

b) What is the probability that ``Ann''(female) and her friend ``Bob''(male) are on the committee and their friends ``Carla''(female) and ``Dan''(male) are also on the committee?

c) Given that ``Carla'' and ``Dan'' have been chosen to be on the committee, what is the probability that ``Ann'' and her friend ``Bob'' are chosen to be on committee?

d) What is the probability that none of ``Ann'',``Bob'',``Carla'', or ``Dan'' are chosen to be on the committee?

Solutions

Expert Solution

a) Probability that a specific male and a female are selected in the committee is computed here as:

= Number of ways to select 1 woman from the remaining 17 women * Number of ways to select 5 men from the remaining 12 men / Total number of ways the selection could be made

b) Now the probability that ``Ann''(female) and her friend ``Bob''(male) are on the committee and their friends ``Carla''(female) and ``Dan''(male) are also on the committee, again here we just need to select 4 men from remaining 11 men as others are already selected.

c) Given that ``Carla'' and ``Dan'' have been chosen to be on the committee, the probability that ``Ann'' and her friend ``Bob'' are chosen to be on committee is computed using bayes theorem as:

= Number of ways that all 4 are in committee / Number of ways that both Carla and Dan are in committee.

d) Probability that none of them are selected.

This is computed by just removing these 4 from 18 women and 13 men

Probability here is computed as:

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A committee of 4 is chosen at random from a group of 7 women 5 men....

A committee of 4 is chosen at random from a group of 7 women 5 men. Find the probability that the committee contains at least one man. without replacement

From a group of 4 women and 6 men, a committee of 4 members will be...

From a group of 4 women and 6 men, a committee of 4 members will be elected. a) How many committees can you choose? b) How many committees can be elected if there should be 3 men? c) How many committees can be elected if there should be at least one woman? d) If you want to choose a directive, that is, a president, vice president, treasurer and secretary, in how many ways can you choose? e) If the whole...

10). From a group of 6 men and 8 women a committee consisting of 4 men...

10). From a group of 6 men and 8 women a committee consisting of 4 men and 3 women is to be formed. How many different committees are possible if: a. 2 of the men refuse to serve together? b. 2 of the women refuse to serve together? c. 1 man and 1 woman refuse to serve together?

A committee of size 3 is to be selected from 6 men and 2 women. (a)...

A committee of size 3 is to be selected from 6 men and 2 women. (a) Find the probability distribution of the number of women selected in the committee, and (b) Find the standard deviation. *

Q1) Select a committee of size 4 from a group of 6 women and 4 men...

Q1) Select a committee of size 4 from a group of 6 women and 4 men if two of the women will only serve if they are together? Q2) Ten people are to be seated in a row at a concert. Four are from California, 3 are from Minnesota and 3 are from Wisconsin. a) How many different seating arrangements are possible? b) How many different seating arrangements are possible if everyone from Wisconsin must sit together? c) How many...

from a group of 8 women and 5 men a committee of 4 members will be...

from a group of 8 women and 5 men a committee of 4 members will be elected a) how many committees can you choose? b)How many committees can be elected if there should be 3 men? c)How many committees can you choose if there should be at least one woman? d)If you want to elect a board, that is, a president, vice president, treasurer, secretary, in how many ways can you choose? e)If you want to take a photo of...

There are 7 women and 5 men in a department. A committee of 5 is to...

There are 7 women and 5 men in a department. A committee of 5 is to be chosen. A. How many ways can this comittee be chosen? B. How many ways can this comitee be chosen if there must be 2 women and 3 men? C. If the comitee is chosen at random, what is the probability that it will consist of 2 women and 3 men?

Based on the video on Men are From Mars, Women are From Venus: 6 Ways Men...

Based on the video on Men are From Mars, Women are From Venus: 6 Ways Men & Women Communicate Differently Respond here with some of the different communication styles men and women exhibit.

A group consists of 6 men and 5 women. Four people are selected to attend a...

A group consists of 6 men and 5 women. Four people are selected to attend a conference. a. In how many ways can 4 men be selected from this group of 11? b. In how many ways can 4 men be selected from the 6 men? c. Find the probability that the selected group will consist of all men. Would this be unusual?

4. A group consist of 6 men and 5 women. Find the number of choosing 5...

4. A group consist of 6 men and 5 women. Find the number of choosing 5 committee members: e) Without condition f) Must have 2 men and 2 women and another person either men or women g) The number of men must exceed the number of women h) Must have at least 1 men and 1 women 6. How many choices are there if we want to make a 5 person committee from 12 persons, if the president has already...

Subjects