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?

2/3

ReplyDeleteThere 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.

1/2

ReplyDeleteYou 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

hey mike.. no ans for this?

ReplyDeletei agree with andy

ReplyDeleteHi 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.

ReplyDeleteThere 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.

aha !! Thanks Mike :-)

ReplyDelete