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Video: Finding the Probability of the Complement of Events

Kathryn Kingham

If an event has a 42% chance of occurring, what is the probability that it does not occur?

02:23

Video Transcript

If an event has a 42 percent chance of occuring, what is the probability that it does not occur? The probability that an event occurs plus the probability that an event does not occur equals one. For example, the probability that it will rain plus the probability that it won’t rain or doesn’t rain equals one. There’s only two choices, either it will rain or it won’t rain. When you add those two chances together, they’ll equal 100 percent or one.

We can represent that like this. The probability of 𝐴 plus the probability of 𝐴 prime equals one. These events are complementary and their sums of probabilities equal to one. Let’s use this formula and plug in the information that we know. The probability of our event is giving us 42 percent. Before we can use this formula, we need to recognise a problem here. The number one is a whole number, but our probability is given in a percent.

We have two choices here. We can convert our percent to a decimal or we can represent our whole number as a percent. For this case, I’m gonna choose to take our number one and convert it to a percent. The whole number one written as a percent equals 100 percent. Now we have 42 percent plus the probability that that does not occur equals 100 percent. We subtract 42 percent from both sides of the equation: 100 percent minus 42 percent equals 58 percent. The probability that our event does not occur equals 58 percent.