Question

If you roll a standard numbered cube, what is the complement of rolling a 2, 3, or 4?

Answer 1

Answer: The complement of an event is the set of all outcomes that are not part of the event. If you roll a standard numbered cube, the complement of rolling a 2, 3, or 4 would be rolling a 1, 5, 6. These are all the outcomes that are not a 2, 3, or 4.

Answer 2

P(A) = 2/6

P(A’) = 4/6

Explanation:

In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A] are mutually exclusive and exhaustive. Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A. The complement of an event A is usually denoted as A′, Aᶜ, ¬A or A. Given an event, the event and its complementary event define a Bernoulli trial: did the event occur or not?

Our complement, A’, would then be “rolls a 1, 2, 3, or 4.” We can illustrate this as follows: The event “rolling a 5 or 6” and its complement “rolling a 1, 2, 3, or 4.”