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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
From the first $100$ natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If the probability that $a - b \ge 10$ is $\frac{m}{n}$, $\gcd(m,n)=1$, then $m+n$ is equal to ______.
Solution
$a - b \ge 10$
Total cases $= 100 \times 99$
Favourable cases $= 1 + 2 + 3 + \cdots + 90$
Required probability
$= \dfrac{1 + 2 + \cdots + 90}{100 \times 99}$
$= \dfrac{90\cdot 91}{2 \cdot 100 \cdot 99}$
$= \dfrac{91}{220}$
$\Rightarrow m+n = 91 + 220 = 311$
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