What is complement in probability

Use the Complement Rule to find the probability that the sum is less than Skip to main content. Search for:. Using the Complement Rule to Compute Probabilities We have discussed how to calculate the probability that an event will happen. Find the probability that the sum of the numbers rolled is less than or equal to 3. Find the probability that the sum of the numbers rolled is greater than 3.

Solution The first step is to identify the sample space, which consists of all the possible outcomes. These would include the following outcomes: , , and So there are only three ways to roll a sum of 3 or less.

Try It 5 Two number cubes are rolled. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less. Example : If the probability of an event is , what is the probability of its complement? The odds of an event is the ratio of the probability of an event to the probability of its complement.

In other words, it is the ratio of favorable outcomes to un favorable outcomes. We say the odds are "3 to 2," which means 3 favorable outcomes to every 2 unfavorable outcomes, and we write 3 : 2. For example, the odds of rolling a 5 or greater are 2 : 4 , which reduces to 1 : 2. Example 1 : If we flip a coin two times, what are the odds for it landing heads at least once? Unfavorable outcomes: 1 -- TT.