| Assertion (A): Cards numbered 5 to 102 are placed in a box. If a card is selected at random from the box, then the probability that the card selected has a number which is a perfect square, is \[\frac{4}{49}\]. |
| Reason (R): Probability of an event E is a number \[P(E)\]such that \[0\le P(E)\le 1\] |
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: B
Solution :
| [b] Clearly, Reason is true. |
| Total number of cards \[=102-5+1=98\] |
| So, total number of possible outcomes= 98 |
| Let E be the event of selecting a card with square number. |
| So, favorable outcomes to E are \[\{9,16,25,36,49,64,81,100\}\]i.e., 8 |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,P(E)=\frac{8}{98}=\frac{4}{49}\] |
| \[\therefore \] Assertion: True; Reason: True but it is not the correct explanation of Assertion. |
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