probability word problem help

S

shelly89

Junior Member
Joined
Oct 17, 2012
Messages
53
Bag A contains five white and four black balls. bag B contains three white balls and two black balls. One ball is drawn from A and is transfered to B, one ball is then drawn from B and turns out to be white, what is the probability that the transferred ball was white?


I dont have any idea where to start with this question, any help appreciated.
 
Hello, shelly89!

Bag A contains 5 white and 4 black balls' bag B contains 3 white balls and 2 black balls.
One ball is drawn from A and is transfered to B.
One ball is then drawn from B and turns out to be white.,
What is the probability that the transferred ball was white?
Click to expand...

This is a Conditional Probability problem.
It requires Bayes' Theorem.

Are you familiar with any of that?
 
shelly89 said:
Bag A contains five white and four black balls. bag B contains three white balls and two black balls. One ball is drawn from A and is transfered to B, one ball is then drawn from B and turns out to be white, what is the probability that the transferred ball was white?
Click to expand...
You want to find \(\displaystyle \mathcal{P}(W_1|W_2)\). That is the probability the first ball was white given that the second ball is white. \(\displaystyle \mathcal{P}(W_1|W_2)=\dfrac{\mathcal{P}(W_1\cap W_2)}{\mathcal{P}(W_2)}\)

To find that we need
\(\displaystyle \mathcal{P}(W_2)=\mathcal{P}(W_2\cap W_1)+\mathcal{P}(W_2\cap B_1)\)

\(\displaystyle =\mathcal{P}(W_2|W_1)\mathcal{P}(W_1))+\mathcal{P}(W_2|B_1)\mathcal{P}(B_1)\)
 
You must log in or register to reply here.
Top