Language: Complement of “At Least One” Let A = the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing event$\overline{A}$.

Three iPhones are selected at random.

A is the event of selecting at least one defective iPhone.

A and $\overline{A}$are said to be complementary when the former denotes the occurrence of the event and the latter denotes the non-occurrence of the event or vice-versa.

Thus, the outcomes of event A are opposite (all elements of sample space except those supportive of A) to $\overline{A}$.

The following property holds true for the probability of complementary events:

$P\left(A\right)+P\left(\overline{A}\right)=1$

A is the event of selecting at least one defective iPhone. Therefore,the number of defective iPhones selected is 1, 2, or 3 in the three randomly selected iPhones.

Thus, is the event of “not” selecting at least one defective iPhone. In other words, it is an event of not selecting any (0) defective iPhone.