25. Working from Home The table shows the results of a survey ...

Question

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.

b. The person is female or does not work from home.

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Accepted Answer

Welcome back, everyone. Apo asked 1750 employees how often they take lunch breaks away from their desks. The results are given below. If one employee is chosen at random, what is the probability that the employee is female or always takes lunch away from their desk? A 0.326. B. 0.120. C. 0.880, and D 0.674. So for this problem, we're looking at two possible events. Let's define them. So the first one is A, it says that If one employee is chosen at random, what is the probability that the employee is female? So let's define A as an employee being a female. And B Takes lunch away from their desk so we can say. Takes Lunch Away From their desk We're going to use the table to find the probability of A or B occurring, so probability of A or B is equal to the probability of A. We're going to use the formula plus the probability of B minus the probability of a intersection B, right? So if our events are not mutually exclusive, then the probability of a intersection B is not 0, and this term is really important. So as define all probabilities. The probability of a now those will be females, right? The total number of females is 1000. So we take 1000 and divide by the total number of employees, and that would be 1750, and this represents the probability of a female. Now, the probability of an employee who takes lunch away from their desk would be the probability of B. Now We're specifically interested in those who always take lunch away from their desk. So we can also define it in our event. And now we're going to analyze the first column. It says always, and the total number of employees is 390. So we have to divide 390 by 1750. So this is the probability that an employee takes lunch away from their desk, always. And now let's define the probability of A and B. That would be the probability of an event that an employee who always takes lunch away from their desk is a female, and that would be 210 based on the table, right? So we divide 210 by the total number of employees, 1750. And now applying the formula, the probability of A or B occurring is equal to 1000. Divided by 1750. Plus 390 divided by 1750 minus 27 divided by 1750, which is equal to 1180. Divided by 1750, or in its decimal form, we can express it as 0.674 rounded to three decimal places, and that we answered to is the. Thank you for watching.

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.
b. The person is female or does not work from home.

Key Concepts

Probability

Union of Events

Complementary Events

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