Question

The probability that an event A happens in one trial of an experiment is $0.4$. Three independent trails of the experiment are performed. The probability that event A least once is

Answer 1

As the probability that event happens is $0.4$ so the probability that event will not happen will be $1-0.4=0.6$ and the events are mutually independent of each other. So, the probability of each event will not affected.

If in all the trials, event will not happen, then probability will be $0.6\times 0.6\times 0.6=0.216$

So, the probability that event will happen atleast one $=1-\left(Probabilityofeventnothappen\right)$

$\Rightarrow P\left(atleastone\right)=1-0.216=\mathrm{0.784.}$

Hence, the answer is $\mathrm{0.784.}$