Multiple choice

A cards is drawn from a pack of $52$ cards. What is the probability that it is a spade or an ace?

  1. $\dfrac{1}{13}$
  2. $\dfrac{1}{14}$
  3. $\dfrac{2}{13}$
  4. $\dfrac{4}{13}$
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D Correct answer
Explanation

There are 13 spades and 4 aces, but the ace of spades is counted twice. Thus, favourable cards = 13 + 4 - 1 = 16, giving probability 16/52 = 4/13.

AI explanation

Using the addition rule of probability, the probability of drawing a spade or an ace is P(Spade) plus P(Ace) minus P(Spade and Ace). There are 13 spades, 4 aces, and 1 card that is both the ace of spades, so the formula becomes 13/52 plus 4/52 minus 1/52. This calculation results in 16/52, which simplifies by dividing by 4 to equal 4/13.

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