# Video: Determining the Probability of Complement of a Given Event

Suppose 𝐴 is an event such that 𝑃(𝐴) = 4/5. Determine the 𝑃(𝐴′).

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### Video Transcript

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

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

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

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

Therefore, the probability of 𝐴 not occurring or 𝑃 of 𝐴 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.