Multiple choice

The integers from 1 to 30 inclusive are written on cards. These cards put in a box and well mixed Prakash picked up one card, What is the probability that his card has a prime number ?

  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{1}{4}$
  3. $\displaystyle \frac{1}{3}$
  4. $\displaystyle \frac{1}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D be Diana's age and J be Jim's age. 3D = 2J + 17. D + J = (3J) - 13. From the second eq: D = 2J - 13. Substitute into the first: 3(2J - 13) = 2J + 17 => 6J - 39 = 2J + 17 => 4J = 56 => J = 14. Then D = 2(14) - 13 = 15. Ages are 15 and 14.

AI explanation

The sample space contains 30 cards. The prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29, giving 10 favorable outcomes. Using the formula for probability, which is the number of favorable outcomes divided by the total number of outcomes, we get 10 divided by 30. This simplifies to 1/3.

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