## Wednesday, March 17, 2010

### Simpler Probability

At least, this should be a little bit simpler than yesterdays problem.

A cloth bag contains a pool ball, which is known to be a solid ball.  A second pool ball is chosen at random in such a way that it is equally likely to be a solid or a stripe ball.  The ball is added to the bag, the bag is shaken, and a ball is drawn at random.  This ball proves to be a solid.  What is the probability that the ball remaining in the bag is also a solid?

1. 2/3

There are three cases where you could draw a solid first, since ball 1 was a solid:

-Ball 2 was a stripe, you drew ball 1.
-Ball 2 was a solid, you drew ball 1.
-Ball 2 was a solid, you drew ball 2.

In 2/3 cases, the remaining ball will be a solid.

2. 1/2

You drew one ball that is solid.

Now when we put the second ball then it was equally likely to be a solid or a stripe bal!!

So it would be the same as that of the probablity of the second ball that we had put.

1/2 + 0 = 1/2

3. hey mike.. no ans for this?

4. i agree with andy

5. Hi Bizzare, I was wondering if anyone would want to rethink this based on the next day's question, but never came back to suggest it. Since I didn't, I'm just going to lay out the answer.

There are four possible outcomes, all equally likely.

* Solid added; original solid drawn.
* Solid added; new solid drawn.
* Stripe added; original solid drawn.
* Stripe added; new stripe drawn.

Since a solid was drawn, we can eliminate the last possibility. That means two out of the three remaining are possible, so the probability is 2/3.

6. aha !! Thanks Mike :-)

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