This is the way that I see the problem (please correct me if I’m wrong).
ANSWER: 1⁄5
We know that the person has an Ace of spades in their hand which means the following are the only combinations the person could have is AH and AS, 2C and AS, 2D and AS. The probability of the person answering the question with “I have an Ace of spades” when the person has the combination of AH and AS is 1⁄2. The probability with 2C and AS is 1 and the probability of 2D and AS is 1 as there is only one ace in these combinations meaning the person would be forced to choose these. There for the probability is (1/2)/(1/2+1+1) which simplifies to 1⁄5. Mathematically this can be shown as:
This is the way that I see the problem (please correct me if I’m wrong).
ANSWER: 1⁄5
We know that the person has an Ace of spades in their hand which means the following are the only combinations the person could have is AH and AS, 2C and AS, 2D and AS. The probability of the person answering the question with “I have an Ace of spades” when the person has the combination of AH and AS is 1⁄2. The probability with 2C and AS is 1 and the probability of 2D and AS is 1 as there is only one ace in these combinations meaning the person would be forced to choose these. There for the probability is (1/2)/(1/2+1+1) which simplifies to 1⁄5. Mathematically this can be shown as:
AH AS P(choose AS)=1/2 P(choose AH)=1/2
2C AS P(choose AS)=1
2D AS P(choose AS)=1
therefore P(both) = (1/2)/(1/2+1+1) = 1⁄5
:)