Q77 / 160 · AP EAMCET 2022 (05 Jul Shift 1) · Mathematics

Two brothers $X$ and $Y$ appeared for an exam. Let $A$ be the event that $X$ has passed the exam and $B$ is the event that $Y$ has passed. The probability of $A$ is $\frac{1}{7}$ and of $B$ is $\frac{2}{9}$. Then, the probability that both of them pass the exam is

  • A
    $\frac{1}{63}$
  • B
    $\frac{2}{35}$
  • Correct answer
    C
    $\frac{2}{63}$
  • D
    $\frac{9}{14}$

Solution

Given, $A$ be the event that $x$ is selected and $B$ is the event that $y$ is selected. $P(A)=\frac{1}{7}, P(B)=\frac{2}{9}$ Let $C$ be the event that both are selected. $P(C)=P(A) \times P(B)$ as $A$ and $B$ are independent events $=\frac{1}{7} \times\left(\frac{2}{9}\right)=\frac{2}{63}$

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

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