Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
Let $\mathrm{S}_{\mathrm{n}}=\sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{k}$ denote the sum of the first $\mathrm{n}$ positive integers. The numbers $\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \ldots \mathrm{S}_{99}$ are written on 99 cards. The probability of drawing a card with an even number written on it is -
MathematicsProbabilityKVPYKVPY 2012 (SB/SX)
Options:
  • A $1 / 2$
  • B $49 / 100$
  • C $49 / 99$
  • D $48 / 99$
Solution:
1154 Upvotes Verified Answer
The correct answer is: $49 / 99$
$1,3,6,10,15,21,28,36,45,55,66,78,91,105$ till 98 terms 48 terms are even and 48 terms odd
$99^{\text {th }}$ term $=\frac{99 \times 100}{2}=$ even
Total even terms $=48+1=49$
Probability $=\frac{49}{99}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.