Video: Determining the Probability of Complement of a Given Event

Suppose ๐ด is an event such that ๐‘ƒ(๐ด) = 4/5. Determine the ๐‘ƒ(๐ดโ€ฒ).

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Video Transcript

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

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

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

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

Therefore, the probability of ๐ด not occurring or ๐‘ƒ of ๐ด 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.

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