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

Question

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 (A) 0.936 (B) 0.784 (C) 0.904 (D) None of these

Tardigrade Admin · Accepted Answer

Given that, P(A) = 0.4, P( overlineA) = 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

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

0.936

0.784

0.904

None of these

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)
$= 1 - (0.6) (0.6) (0.6) = 1 - 0.216 = 0.784$

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