Question

The probability of an even happens in one trial of an experiment is $0.3$. Three independent trials of the experiments are performed. Find the probability that the event A happens at least once.

• A. $0.657$
• B. $0.965$
• C. $0.796$
• D. $0.509$

Answer 1

The correct option is A $0.657$

Probability of an event happens in $1$ trial $=0.3$

$\Rightarrow$ Probability of an event that don't happen in $1$ trail $=0.7$

$\Rightarrow$ Total number of trial , $n=3$

$\Rightarrow$ $p=0.3$ $q=0.7$

$\Rightarrow$ By Bernoulli's theorm, $P={}^n{C}_r{p}^r{q}^{n-r}$

P ( Event happens alteast once )

$={}^3{C}_1{\left(0.3\right)}^1{\left(0.7\right)}^2+{}^3{C}_2{\left(0.3\right)}^2\left(0.7\right)+{}^3{C}_3{\left(0.3\right)}^3{\left(0.7\right)}^0$

$=0.441+0.189+0.027$

$=0.657$

Hence, the answer is $\mathrm{0.657.}$