Question

explain how the complement can be used to find the probability of getting at least one item of a particular type.

choose the correct answer below

a. the complement of \at least one\ is \all\ so, the probability of getting at least one item is equal to 1 - p(all items)

b. the complement of \at least one\ is
one\ so, the probability of getting at least one item is equal to 1 - p(none of the items)

c. the complement of \at least one\ is
one\ so, the probability of getting at least one item is equal to p(none of the items) - 1

d. the complement of \at least one\ is \all\ so, the probability of getting at least one item is equal to p(all items) - 1

Explanation:

For probability problems, the complement rule states that \(P(A)=1 - P(\text{complement of }A)\). The event "at least one" means \(1\) or more. Its complement is "none" (i.e., \(0\)). So, using the formula \(P(\text{at least one})=1 - P(\text{none})\).

Answer:

B. The complement of "at least one" is "none" So, the probability of getting at least one item is equal to \(1 - P(\text{none of the items})\)