(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

You walk into your class the first day of classes, and you notice that

there are 30 men and 20 women in the class already. Let's suppose you decide to choose

two people from the class to be your study partners.

If you choose your study partners at random, and given that at least one of your

study partners is a woman, what is the probability of the event E that both of them

will be women?

A. 0.3167

B. 1.9%

C. 0.2405

D. 0.1901

2. Relevant equations

In my Solution

3. The attempt at a solution

This seems like a simple problem but I cannot seem to get the numbers available as choices.

My logic is is, W represents the event that you have picked a woman, and E represents that both of your partners will be women then.

[tex]P(E|W)=\frac{P(E \cap W)}{P(W)}[/tex]

So the numerator can simplify to..

[tex]P(E|W)=\frac{P(E)}{P(W)}[/tex]

This is because if E occurs, then W must have occured.

So..

[tex]P(E)=\frac{\binom{20}{2}}{\binom{50}{2}}[/tex]

and

[tex]P(W)=\frac{\binom{20}{1}}{\binom{50}{2}}[/tex]

But this doesn't work because the ratio of these two (From the formula) gives a number larger than one. Where am I going wrong? Do I use Bayes theorem?

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# Homework Help: Probability: Choosing a girl from a group

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