There’s an easy way to figure out the probability: say that the person holding the cards flips a coin. If he has two Aces, when asked to pick one, heads means he picks the Ace of Spades, and tails means he picks the Ace of Hearts.
There are twelve possible outcomes: 6 possible two-card hands times 2 possibilities for the coin flip. The person’s responses have ruled out all but five: 1) heads, AS, AH; 2) heads, AS, 2C; 3) tails, AS, 2C; 4) heads, AS, 2D; 5) tails, AS, 2D. Each is equally likely and he has two Aces in 1), so the probability must be 1⁄5.
(We don’t have the same information as in Scenario 1 because the coin flip made it less likely that he has two Aces, as Unknowns explained.)
There’s an easy way to figure out the probability: say that the person holding the cards flips a coin. If he has two Aces, when asked to pick one, heads means he picks the Ace of Spades, and tails means he picks the Ace of Hearts.
There are twelve possible outcomes: 6 possible two-card hands times 2 possibilities for the coin flip. The person’s responses have ruled out all but five: 1) heads, AS, AH; 2) heads, AS, 2C; 3) tails, AS, 2C; 4) heads, AS, 2D; 5) tails, AS, 2D. Each is equally likely and he has two Aces in 1), so the probability must be 1⁄5.
(We don’t have the same information as in Scenario 1 because the coin flip made it less likely that he has two Aces, as Unknowns explained.)