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

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

IIT JEEIIT JEE 1980Probability

Solution:

Given that, $P(A) = 0.4, P(\overline{A}) = 0.6$
$P$(the event A happens at least once)
$= 1 - P$ (none of the event happens)
$= 1 - (0.6) (0.6) (0.6) = 1 - 0.216 = 0.784$