Question

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

• A. 0.936
• B. 0.784
• C. 0.904
• D. none of these

Answer 1

The correct option is B 0.784

probability that an event happens in one trial of an experiment $=0.4$

Probability of that event not happening in one trial $=1-0.4=0.6$

Three independent trials of the experiment are performed.

$\text{probability that the event happens at least once in three trails}$

$=\text{1 - Probability of that event not happening in all three trials}$

$=1-\left(0.6\right)\times \left(0.6\right)\times \left(0.6\right)$

$=1-0.216$

$=0.784$

Hence, option $B$ is correct.