A ticket is drawn at random from 20 tickets numbered 1 to 20. Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Probability that the number is a multiple of 5, given that it is even | (I) | \(\displaystyle\frac{1}{4}\) |
| (B) | Probability that the number is even, given that it is a multiple of 5 | (II) | \(\displaystyle\frac{7}{10}\) |
| (C) | Probability that the number is a prime, given that it is odd | (III) | \(\displaystyle\frac{1}{5}\) |
| (D) | Probability that the number is a multiple of 3, given that it is greater than 12 | (IV) | \(\displaystyle\frac{1}{2}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
In each case the given condition leaves a reduced sample space of equally likely numbers, and the probability is the share of those numbers that have the required property.
(A) Probability that the number is a multiple of 5, given that it is even
This matches (III) \(\frac{1}{5}\).
The even numbers are 2, 4, …, 20 (10 numbers). Of these, only 10 and 20 are multiples of 5:
\( \displaystyle P = \frac{2}{10} = \frac{1}{5} \)
(B) Probability that the number is even, given that it is a multiple of 5
This matches (IV) \(\frac{1}{2}\).
The multiples of 5 are 5, 10, 15, 20 (4 numbers). Of these, 10 and 20 are even:
\( \displaystyle P = \frac{2}{4} = \frac{1}{2} \)
(C) Probability that the number is a prime, given that it is odd
This matches (II) \(\frac{7}{10}\).
The odd numbers are 1, 3, 5, …, 19 (10 numbers). The primes among them are 3, 5, 7, 11, 13, 17, 19 (1 is not a prime):
\( \displaystyle P = \frac{7}{10} \)
(D) Probability that the number is a multiple of 3, given that it is greater than 12
This matches (I) \(\frac{1}{4}\).
The numbers greater than 12 are 13 to 20 (8 numbers). Of these, 15 and 18 are multiples of 3:
\( \displaystyle P = \frac{2}{8} = \frac{1}{4} \)