Question Video: Determining the Probability of Complement of a Given Event Mathematics • Third Year of Preparatory School

Video Transcript

The probability that an event occurs is nine tenths. What is the probability that the event does not occur?

We need to think about the nature of probability. This is what I mean by that. The probability that an event occurs plus the probability that an event does not occur will always equal one.

We know that the probability of the event occurring is nine tenths. If we add the probability that the event does not occur to nine tenths will be equal to one. If we subtract nine tenths from one, we will find out the probability that the event does not occur. One minus nine tenths equals one tenth.

If we wanted to check our answer, we can add the probability that the event occurs plus the probability that the event does not occur. Nine tenths that it does occur plus one tenth that it doesn’t occur equals one. We can say with certainty that the probability the event does not occur is one tenth.