Q254 / 270 · NDA 2022 (Phase 2) · Mathematics

Two numbers $x$ and $y$ are chosen at random from a set of first 10 natural numbers. What is the probability that $(x+$ $y)$ is divisible by 4 ?

  • A
    $\frac{1}{5}$
  • Correct answer
    B
    $\frac{2}{9}$
  • C
    $\frac{8}{45}$
  • D
    $\frac{7}{45}$

Solution

$n(s)=10 \times 9=90$ Sum of $x+y$ is divisible by 4 are $\begin{aligned} & (1,3),(1,7),(2,6),(2,10),(3,1),(3,5),(3,9),(4,8) \\ & (5,3),(5,7),(6,2),(6,10),(7,1),(7,5),(7,9),(8 \\ & 4),(9,3),(9,7),(10,2),(10,6) \\ & n(E)=20 \\ & \therefore P(E)=\frac{20}{90}=\frac{2}{9} \end{aligned}$

Hence, the correct answer is option: 'B'.

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