In a standard deck of 52 playing cards, what is P(ace | the card drawn is a spade)?

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Multiple Choice

In a standard deck of 52 playing cards, what is P(ace | the card drawn is a spade)?

Explanation:
Knowing the card drawn is a spade means we’re looking at conditional probability within the 13 spades. Each spade is equally likely, and among these 13 cards only one is an ace (the ace of spades). So the chance the card is an ace given that it’s a spade is 1 out of 13. In probability terms, P(ace | spade) = P(ace ∩ spade) / P(spade) = (1/52) / (13/52) = 1/13.

Knowing the card drawn is a spade means we’re looking at conditional probability within the 13 spades. Each spade is equally likely, and among these 13 cards only one is an ace (the ace of spades). So the chance the card is an ace given that it’s a spade is 1 out of 13. In probability terms, P(ace | spade) = P(ace ∩ spade) / P(spade) = (1/52) / (13/52) = 1/13.

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