Question

The probability of happening of an event in an experiment is 0.4. The probability of happening of the event atleast once, if the experiment is repeated 3 times under similar conditions is

• A. $0.216$
• B. $0.784$
• C. $0.64$
• D. $0.32$

Answer 1

Answer: (B)

$0.784$

$p=0.4$
$q=1-0.4=0.6$
Hence the required probability is
${}^3{C}_1\left(0.4{)}^1\right(0.6{)}^2+{}^3{C}_2\left(0.4{)}^2\right(0.6{)}^1+{}^3{C}_3\left(0.4{)}^3\right(0.6{)}^0$
$=3\left(0.4\right)\left(0.36\right)+3\left(0.16\right(0.6\left)\right)+\left(0.064\right)$
$=0.432+0.288+0.064$
$=0.784$