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

A bag contains 4 balls. Two balls are drawn at random, and are found to be white. What is the probability that all balls are white?

2. Relevent equations

At school, I'm currently learning Bayes' theorem, probability disribution and Bernoulli trials.

3. The attempt at a solution

The 4 balls can be

1) all white

2) 3 white, 1 non-white

3) 2 white, 2 non-white

4) 1 white, 3 non-white

5) all non-white

P(all white)=1/5

But given, two balls taken at random are white.

I can't figure out what to do next. When I ignore the 2 white balls, I get the answer as 1/3 which is wrong according to my text book.

[Edit]: I got it!

A-2 balls taken are white

E_{1}-4W

E_{2}-3W, 1Non-white

E_{3}-2W, 2N

E_{4}-1W, 3N

E_{5}-4N

P(E_{1}/A)= {P(E_{1})P(A/E_{1})} / {P(E_{1})P(A/E_{1})+...+P(E_{5})P(A/E_{5})}

={1/5*1} / {1/5*1 + 1/5*3C2/4C2 + 1/5*2C2/4C2 + 1/5*0 + 1/5*0}

=3/5

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# Homework Help: Probability all balls are white.

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