Question

Suppose that an experiment is repeated four times. A certain event has probability in a single repetition of the experiment. What is the probability that it occurs at least once?

729/10,000
3,439/10,000
2,187/10,000

Answer 1

the probability is missing but let's pretend

P(A) = probability of the event happening one time

"the event occurs at least once" is the opposite of "the event does not occur at all". probability that the event does not occur is much easier to calculate.

the probability of the event *not* happening is 1 - P(A)

the probability of the event not happening 4 times in a row is simply [1 - P(A)]^4

and the exact opposite of this scenario (the event happens at least once in four tries) is simply 1 - [1 - P(A)]^4