QUESTION 4 A deck has four cards: the ace and deuce of hearts, and the ace and d

Question

QUESTION 4 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 "1 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? Hint: If the deck is: then the possible two-card hands that Alice can get are: A 2 hands have tuo aces in them? Hoe many hands inchude an ace? How many hands inchude the Ace of Spades

Explanation / Answer

unconditional probability of receiving two ace hand is 1/6

When we know that 1 card is an Ace then probaiblity will increase to 1/5

When we know that 1 card is an ace of spades then probability will be 1/3

As knowing particular card of ace will refines the information set we have from size 5 to 3 which helps to increase success probability from 1/5 to 1/3...(Size 3 means only 3 possible pairs out of 6 which contain Card ace with spades)

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