Multiple choice

In a lottery of 50 tickets numbered 1 to 50, 2 tickets are drawn simultaneously. The probability that both the tickets drawn have prime numbers is

  1. 3 245

  2. 21 245

  3. 3 25

  4. 7 245
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B Correct answer
Explanation

There are 15 prime numbers between 1 and 50. The probability of choosing 2 prime numbers from 50 tickets is given by (15C2) / (50C2) = (15 * 14) / (50 * 49) = 210 / 2450 = 21 / 245, which simplifies to 3 / 35.

AI explanation

Using the definition of classical probability, we find the number of favorable outcomes divided by the total number of outcomes. There are 15 prime numbers between 1 and 50, so the number of ways to choose 2 prime tickets is 15 factorial divided by the product of 2 factorial and 13 factorial, which equals 105. The total ways to choose any 2 tickets from 50 is 50 factorial divided by the product of 2 factorial and 48 factorial, which equals 1225. The probability is 105 divided by 1225, which simplifies to 21 divided by 245.

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