Multiple choice

A number is chosen at random from the list of prime numbers less than $50$. The chance that it has its square greater than $100$ is

  1. $1/5$
  2. $4/5$
  3. $3/5$
  4. $11/15$
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D Correct answer
Explanation

Primes < 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 (15 total). Squares > 100: 11^2=121, 13^2=169, etc. Primes with square > 100 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 (11 total). Probability = 11/15.

AI explanation

The prime numbers less than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47, giving a total of 15 primes. The primes whose squares are not greater than 100 are 2, 3, 5, and 7, as their squares are less than or equal to 100. This leaves 15 minus 4, which is 11 prime numbers that have squares greater than 100. Therefore, the required probability is 11 divided by 15.

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