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Question: A deck has four cards: the ace and deuce of hearts, and the ace and deuce of spades. After a fair shuffle of the deck, two cards are dealt to Alice.

1.Alice then tells Bob "I have an ace".

2. She then says "I have the ace of spades"

The situation is similar if Alice says "I have the ace of hearts".

Puzzle: Why should finding out which particular ace it is raise the conditional probability of Alice having two aces?

To answer this puzzle: do the following:

1. Calculate the unconditional probability of receiving a two-ace hand.

2. Calculate the conditional probability of a two-ace hand when Alice says "I have an ace".

3. Calculate the conditional probability of a two-ace hand when Alice says "I have the ace of spades".

4. Compare the two calculations. What happened?

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M92583718

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