Multiple choice

A card is drawn from a well shuffled ordinary deck of 52 playing cards. The card drawn is found to be a spade. Then the probability that the card is an ace is

  1. $\displaystyle \frac{1}{13}$
  2. $\displaystyle \frac{1}{52}$
  3. $\displaystyle \frac{1}{4}$

  4. none of these
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A Correct answer
Explanation

There are 13 spades in a deck. Only one of them is an ace. Given the card is a spade, the probability it is an ace is 1/13.

AI explanation

Given the condition that the drawn card is a spade, we apply the conditional probability formula. The sample space is reduced to the 13 spades in the deck. Among these 13 spades, exactly 1 card is the ace of spades, so the required probability is 1 out of 13, which equals 1/13.

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