Multiple choice

All the cards in an ordinary deck of 52 cards are numbered from 1 to 52 If a card is drawn at random from the deck then what is the probability that it will have a prime number?

  1. $\displaystyle \frac{7}{26}$
  2. $\displaystyle \frac{1}{4}$
  3. $\displaystyle \frac{3}{13}$
  4. $\displaystyle \frac{15}{52}$
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D Correct answer
Explanation

Primes between 1 and 52: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. There are 15 primes. Probability = 15/52.

AI explanation

To find the probability using the classical definition, we count the prime numbers between 1 and 52, which are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. This gives a total of 15 favorable outcomes out of 52 possible cards. The probability of drawing a prime-numbered card is therefore 15/52.

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