### Video Transcript

Suppose ๐ด is an event such that the probability of ๐ด equals four-fifths. Determine the probability of ๐ด dash.

Well the probability of ๐ด dash means the probability of ๐ด not occurring. This means that ๐ด and ๐ด dash are complementary. Therefore, the sum of their probabilities equals one.

We can write this as an equation. The probability of ๐ด plus the probability of not ๐ด equals one. As we were told in the question, that the probability of ๐ด occurring was four-fifths, then four-fifths plus the probability of not ๐ด equals one.

Subtracting four-fifths from both sides of this equation gives us that the probability of ๐ด not occurring is one minus four-fifths. One minus four-fifths is equal to one-fifth.

Therefore, the probability of ๐ด not occurring or ๐ of ๐ด dash is equal to one-fifth. This method can be used to calculate the probability of any event not occurring. We simply subtract the probability the event occurs, in this case four-fifths, from one.