I have tried but I didn't get much clearer about the question. That's why I posted this here.
Actually, it really helps if you show us even the little that you tried, because it gives us a place to start; I asked specific questions in the hope that you would be willing to go along and take that first step. (Theorems are not always stated in the same way, and using the form you were taught would make it easier to be sure we are communicating clearly.)
But at least you've indicated where in the
problem we can start:
The very second sentence of questions created trouble for me.
# Bag M consists of 5 red and 4 white balls and bag N consists of 4 red and 4 white balls. A bag is selected at random and a ball is transferred to other. Two balls are drawn one after another from bag N. Find the probability that
a) They are different color.
b) They are same color if
i) first ball is returned back.
ii) first ball is not returned back.
As pka suggested, let's look only at
(ai) to keep it simple.
I will assume "the second sentence" that confuses you is the one in
bold. I'll try restating the problem as I understand it, focusing on that:
We have two sets of balls:
- M = {R,R,R,R,R,W,W,W,W}
- N = {R,R,R,R,W,W,W,W}
Phase 1: We select one of these sets (say, M), then select one ball from there (say, R) and move it to the other set (in this case, N).
Phase 2: We select a ball from set N, put it back, stir them up, and again pick a ball from set N. (This is the meaning of "the first ball is returned back"; the usual phrase for this is "with replacement". It means that the probabilities for the second ball are unchanged.)
So, as pka indicated, there are four possibilities for what happens in phase 1: move Red from M, move White from M, move Red from N, move White from N. Each of these has a probability of occurring, and leaves N in a particular state (what balls are there). List the probability of each of these things happening, and what balls are in N.
Now, in each case, you can find the probability that two different-colored balls are chosen.
Then, think about how to put these probabilities together.
One thing I hope you can see is that this is not a simple problem; I don't immediately see an answer. What I've done so far is the way to start: just think about what's happening, and restate the problem to make it clearer. Don't expect to just plug numbers into a formula. That should be encouraging to you: The fact that you didn't get the answer quickly doesn't mean that you are dumb.
