26. Eye Survey The table shows the results of a survey that as...

Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

d. The person is male or does not wear glasses.

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Accepted Answer

Welcome back, everyone. A poll of 2650 adults asks whether they prefer tea, coffee, both, or neither. The results are as follows. If one adult is is selected at random, what is the probability that the person is male or does not prefer coffee? A says 0.725. B 0.275, C 0.625, and D 0.375. In this problem, we're going to define two events. The first one is going to be that the selected person is male. So we're going to define A as male. And B will be that the person does not prefer coffee. We can say it does not. Prefer Coffee Our goal in this problem is to identify the probability of A or B occurring, and we can write our formula. We take the probability of A. At the probability of B. And subtract the probability of A and B occurring at the same time. So, now, what we have to do is simply identify the probability of A occurring. Those will be males, right? And we know that the total number of males based on the first row is 1,487. So, this is the number of favorable outcomes, and we have to divide by the total number of people, 2650. So this ratio gives us the probability of a male. What we have to do from here is simply identify the probability of B occurring and also be. Adults who do not prefer coffee. We know that the total number of adults who prefer coffee only is 1,123, and we also know that. Those who prefer both tea and coffee correspond to 398. So to find the number of adults who do not prefer coffee, we can basically take the total number 2650, subtract 1,123, and subtract 398, right? So essentially we get a total number of 1,129. Those would be our favorable outcomes for the event B 1129, and we have to divide by 2650. And now from here we can simply identify the probability of A and B occurring at the same time. Specifically, were interested in males who do not prefer coffee. Now, for this part, we have to first of all identify our favorable outcomes, and what we can do is simply consider the first row, right? Specifically, we're considering the males, and we're going to add those who prefer tea only, right? And neither because those two categories exclude males. Who actually prefer coffee, so the number of favorable outcomes would be 95 plus 599 divided by 2650 or simply speaking, we get 694 divided by 2650. So now we have all of the parameters needed to solve this problem. Let's identify the probability of A or B occurring. We take 1,487. We then add 1,129 and subtract 694 and then divide everything by the common denominator of 2650. We get 1,922 divided by 2650, which is 0.725, and it corresponds to the answer choice A. Thank you for watching.

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.
d. The person is male or does not wear glasses.

Key Concepts

Probability

Union of Events

Complementary Events

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