| Assertion (A): Consider a pack of cards that are numbered from 1 to 52. If a card is drawn at random from the pack, then the probability that it will have a prime number is \[\frac{7}{26}\]. |
| Reason (R): From 1 to 52, there are 15 prime numbers. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: D
Solution :
| [d] Clearly. Reason is true. |
| Now, total number of outcomes = 52 |
| Prime numbers from 1 to 52 are |
| \[\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\}\] |
| So, favourable number of outcomes =15 |
| \[\therefore \] Required probability \[=\frac{15}{52}\] |
| \[\therefore \] Assertion : False; Reason : True. |
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