Question

In: Statistics and Probability

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?

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 2 years ago

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