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?
I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Wednesday, March 17, 2010
Subscribe to: Post Comments (Atom)
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.
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
hey mike.. no ans for this?ReplyDelete
i agree with andyReplyDelete
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.ReplyDelete
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.
aha !! Thanks Mike :-)ReplyDelete