Multiple choice

A bag contain tickets numbered from $1$ to $20$. Two tickets are drawn. Find the probability that On one there is a prime number and on the other there is a multiple of $4$.

  1. $\dfrac {4}{19}$
  2. $\dfrac {3}{19}$
  3. $\dfrac {5}{19}$
  4.  None of these

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A Correct answer
Explanation

Total ways to choose 2 tickets from 20 is 20C2 = 190. Primes are {2, 3, 5, 7, 11, 13, 17, 19} (8 total). Multiples of 4 are {4, 8, 12, 16, 20} (5 total). Ways to pick one prime and one multiple of 4 = 8 * 5 = 40. Probability = 40/190 = 4/19.

AI explanation

The total number of ways to draw 2 tickets from 20 is 20C2, which equals 190. The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19, giving 8 options. The multiples of 4 are 4, 8, 12, 16, and 20, giving 5 options, and multiplying 8 by 5 gives 40 favorable pairs. The probability is 40 divided by 190, which simplifies to 4/19. The result is 4/19.