Question

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

• A. $0.784$
• B. $0.865$
• C. $0.706$
• D. $0.50$

Answer 1

Answer: (A)

$0.784$

As the probability that an 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 probability of each event will not get affected.

If in all the three 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 at least once =$1-\left(\text{probability of event not happen}\right)$

$⟹P\left(\text{at least once}\right)=1-0.216=0.784$