Answer:
I can help you solve this statistics problem. Here are the steps I followed:
First, I looked at the Venn diagram and the numbers in it. The diagram shows the number of brides and grooms in a sample of 100 people who attended a wedding expo. The circle for brides has 40 people, the circle for grooms has 30 people, and the overlap between the circles has 10 people. This means that there are 10 couples who are both brides and grooms in the sample.
Next, I answered the first question, which asks whether the events “bride” and “groom” are mutually exclusive. Mutually exclusive events are events that cannot happen at the same time. For example, flipping a coin and getting heads or tails are mutually exclusive events, because you cannot get both at once. In this case, the events “bride” and “groom” are not mutually exclusive, because there are some people who are both brides and grooms in the sample. Therefore, the answer to the first question is No.
Then, I answered the second question, which asks for the probability that a randomly selected person from the sample is a bride or a groom. Probability is the measure of how likely an event is to happen. It is calculated by dividing the number of favorable outcomes by the number of possible outcomes. In this case, the number of favorable outcomes is the number of people who are either brides or grooms in the sample. To find this number, we need to add the number of brides and the number of grooms, but subtract the number of people who are both brides and grooms, because they are counted twice. This is called the addition rule for non-mutually exclusive events. Therefore, the number of favorable outcomes is:
40 + 30 - 10
= 60
The number of possible outcomes is the total number of people in the sample, which is 100. Therefore, the probability that a randomly selected person from the sample is a bride or a groom is:
60 / 100
= 0.6
This means that there is a 60% chance that a randomly selected person from the sample is a bride or a groom. Therefore, the answer to the second question is 0.6.
I hope this helps you understand how to solve this problem.