Elementary probabilty problem
- From: Bipp <bipp@xxxxxxxxxxxxxxxx>
- Date: Mon, 16 Jan 2006 12:58:13 GMT
There's a deck of 26 cards, each one with a different letter of the alphabet on one side. Someone randomly picks 10 cards from the deck without showing them to me. I ask him two questions.
First question: "Is there at least one of the three letters A, B, C in your hand?"
Answer: "Yes."
In the following comments, "P(X)" means "probability that letter X is in the hand."
At this point, I can infer that P(A) = P(B) = P(C). Intuitively, I would say that the probability is 1/3, but I think some elementary combinatorial analysis formula would show that the exact value may be slightly different. I haven't done this in years and I'm rusty. How do I calculate it?
Second question: "Is the letter C in your hand?"
If the answer is "no", then P(C) becomes 0. From that new information, I would infer that P(A) and P(B) become 1/2 roughly. How do I calculate the exact probability?
If, instead, the answer is "yes", then P(C) becomes 1. Does this new information change P(A) and P(B)? Intuitively, I would guess that P(A) and P(B) may slightly decrease at this point. I don't trust my intuition. How do I calculate this?
Thanks for any help,
Bipp .
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