Example of Compound Events
Let's look at an example of compound events to see how to calculate more than one event occurring. Wendy and Kim are playing a new deluxe board game titled ED Portalopoly. It is Wendy's turn and she needs to roll the two dice and get both to be a six in order to land on the jackpot. What is the probability that Wendy will roll a six and then roll another six?
To start this problem, we need to calculate each event separately. The total number of outcomes on the dice is six and the number of favorable outcomes is one, because there is only one six on a dice. So, the probability of Wendy getting a six on her first roll is 1 out of 6.
Next, we need to calculate the probability of Wendy getting a six on her second roll. Since these dice are the same, the probability of getting a six on the second roll will also be 1 out of 6. Now that we know the probability of both events happening, we need to multiply these two fractions together. So 1/6 x 1/6 = 1/36. So, the probability of Wendy rolling both dice and getting a six on both is 1/36.
Probability of Complementary Events
Complementary events are another type of event in which we can calculate the probability. Complementary events are events that add together to equal a whole or one. For example, if the probability of it raining today were 2/5, what would the probability be of it not raining? The probability of it not raining would be 3/5, because 2/5 + 3/5 would equal 5/5 or one whole. We know that there are only two choices: it will either rain or not rain.
Example of Complementary Events
Let's check back on Wendy and Kim playing everyone's favorite board game, ED Portalopoly. It is now Kim's turn to roll. If she rolls two dice that add together to equal eight, she will land in jail. Wendy is hoping that Kim lands in jail on this turn. What is the probability that Kim will not roll two dice whose sum is eight?
Wendy needs to first calculate the probability that Kim will roll the two dice and get a sum of eight. To find this probability, she will use the formula: number of favorable outcomes over the number of total outcomes.
Since Kim is rolling two dice and each dice has six sides, there are 36 total outcomes that she can get. To find the number of favorable outcomes, Wendy decides to list out possible ways that the two dice can add to eight. She knows that Kim could roll a 2 + 6, or a 3 + 5, or a 4 + 4, or a 5 + 3 or a 6 + 2. She can see that there are only five different ways to roll two dice whose sum will be eight. Wendy now knows that the probability of Kim rolling two dice and getting a sum of eight is 5 out of 36, or 5/36.
Wendy also wants to know the probability of Kim not getting the two dice to add together to equal eight. These two events are complementary, because they will equal 1 or 36/36. Since the probability of Kim getting the sum of eight was 5/36, we can subtract to find the probability of her not getting the sum of eight.
36/36 - 5/36 = 31/36. The probability of Kim not rolling the two dice and getting the sum of eight is 31/36, so the chance that Kim does not land in jail on her next turn is 31/36.
Lesson Summary
In this lesson, we looked at three different types of probability. The probability of simple events is finding the probability of a single event occurring. When finding the probability of an event occurring, we will use the formula: number of favorable outcomes over the number of total outcomes.
Compound events involve the probability of more than one event happening together. With compound events, we will use the same formula to calculate the probability of each event occurring. Once we find the probability of each event, we will multiply these probabilities together. And the last one was complementary events. Complementary events are events that add together to equal a whole or one.