- #1
Swetasuria
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Homework Statement
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.
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 textbook.
[Edit]: I got it!
A-2 balls taken are white
E1-4W
E2-3W, 1Non-white
E3-2W, 2N
E4-1W, 3N
E5-4N
P(E1/A)= {P(E1)P(A/E1)} / {P(E1)P(A/E1)+...+P(E5)P(A/E5)}
={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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