Hey, everyone. In this problem, we're given a data table, and we're told that this table shows the outfits of 300 observed people on a given day. And we want to know if one person is randomly selected from this group of 300 people, what is the probability that they will either be wearing shorts or wearing a green shirt? Now, this might look overwhelming just because there's a lot of data, but let's go ahead and interpret it together. So we see that of the people that are wearing shorts, we come to a total of 188 out of those 300 people that are wearing shorts. Now for our second event, wearing a green shirt: there are 106 total people wearing a green shirt, and we can see that breakdown. This is a great way to visualize non-mutually exclusive events because we see this region of overlap here where both of these things are happening. People are wearing a green shirt with shorts, so both of these events happen together.
Whenever we're dealing with events that are non-mutually exclusive, we know that we need to account for that region of overlap when calculating the probability. So we know that the probability of our events A or B happening is equal to adding those 2 events together, so taking the probability of A; in this case, we'll refer to wearing shorts as event A, and then adding that with the probability of event B; in this case, wearing a green shirt, and then subtracting that region of overlap. So, subtracting the probability of A and B happening, just as we see in our table here. People are doing both event A and event B.
Now we can go ahead and use our data to fill in the gaps here and calculate our final probability. So for the probability of event A, we know that there are 188 out of 300 total people wearing shorts. We want to take that 188, put it over a total of 300. Then we want to add that together with our probability of event B. So we see that there are 106 total people wearing a green shirt. So we can take that 106, and again, put it over our total of 300. Then finally, we want to subtract that region of overlap, the people that are doing both of these events: wearing shorts with a green shirt. So we're going to take that number of 89 and put it over our total as well, so 89 over 300. Now from here, we're just left to do this calculation. So I can go ahead and add these two values together, and that gives me a number of 294 over 300. That's a lot of people doing both of those events, but I need to subtract that region of overlap. So subtracting that 89 over 300 doing this subtraction, I end up with a value of 205 over 300. It's still a significant amount of people, but not quite so many. Now we can go ahead and reduce this fraction to 41 over 60. Or if you want to express this as a decimal, this goes down to 0.68 as our final answer. So, for one randomly selected person from this group of 300, the probability that they will be wearing shorts or a green shirt, maybe even both, is 0.68. Thanks for watching, and I'll see you in the next one.