Multiple choice

From a pack of $52$ cards one card drawn at random. What is the probability that the card drawn is a ten or a spade?

  1. $\displaystyle \frac{4}{13}$
  2. $\displaystyle \frac{1}{4}$
  3. $\displaystyle \frac{1}{13}$
  4. $\displaystyle \frac{1}{26}$
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A Correct answer
Explanation

P(Ten or Spade) = P(Ten) + P(Spade) - P(Ten of Spades). P(Ten) = 4/52. P(Spade) = 13/52. P(Ten of Spades) = 1/52. Result = (4+13-1)/52 = 16/52 = 4/13.

AI explanation

Using the addition theorem of probability, we calculate P(A union B) as P(A) plus P(B) minus P(A intersection B). The probability of drawing a ten is 4/52, the probability of drawing a spade is 13/52, and the probability of drawing the ten of spades is 1/52. Adding these gives 4/52 plus 13/52 minus 1/52 to equal 16/52. This fraction simplifies to 4/13, which is the probability that the card drawn is a ten or a spade.

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