Q48 / 160 · AP EAMCET 2010 · Mathematics

If $A_i(i=1,2,3, \ldots, n)$ are $n$ independent events with $P\left(A_i\right)=\frac{1}{1+i}$ for each $i$, then the probability that none of $A_i$ occurs is

  • A
    $\frac{n-1}{n+1}$
  • B
    $\frac{n}{n+1}$
  • C
    $\frac{n}{n+2}$
  • Correct answer
    D
    $\frac{1}{n+1}$

Solution

The required probability $=P\left(\bar{A}_1 \cap \bar{A}_2 \cap \ldots \cap \bar{A}_n\right)$ $=P\left(\bar{A}_1\right) P\left(\bar{A}_2\right) \ldots P\left(\bar{A}_n\right)$ $=\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \ldots \cdot \frac{n}{n+1}$ $=\frac{1}{n+1}$

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

Relevant Questions