Question

Let $E_1,E_2,E_3.....E_n$ be n independent events such that $P\left(E_i\right)=\frac{1}{i+1}i=1,2,.....,n$.The probability atleast one of the event occur is

• A. $\frac{n}{n+1}$
• B. $\frac{1}{n}$
• C. $\frac{1}{n+1}$
• D. None of these

Answer 1

The correct option is A $\frac{n}{n+1}$

$P\left(E_i\right)=\frac{1}{i+1}\Rightarrow P\left(\overline{E_i}\right)=\frac{i}{(i+1)}$
Probability that No event occurs $\left(P\right(\overline{E})=P(E_1).P(E_2)....P(E_n)=\frac{1}{n+1}$
$P\left(E\right)=\frac{n}{n+1}$