Politics The responses of 1500 U.S. adults to a survey that as...

Question

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

b. Randomly selecting a person from the sample who is conservative or very conservative

Bar graph showing survey results on political viewpoints, with 'Moderate' having the highest response at 435.

Accepted Answer

Hi, everyone. Let's take a look at this practice problem. This problem says a company surveyed 1500 employees about their job satisfaction levels. The responses were categorized into the following groups very satisfied, satisfied, neutral, dissatisfied, and very dissatisfied. The survey results are shown in the given Pareto chart. Find the probability that a randomly selected employee from the sample is satisfied or very satisfied. And below the problem we're given ourrato chart. And on the X-axis, we have our categories, and they are from left to right, very satisfied, satisfied, neutral, dissatisfied, and very dissatisfied. On the left Y axis, we have the number of employees that fell into each category. So for very satisfied, we have 400, for satisfied, we have 350. For neutral, we have 300, for dissatisfied, we have 250, and for very dissatisfied, we have 200. We also have a line on our chart that shows an increasing trend, and it begins at a value of approximately 27% on the very satisfied category, and ends at 100% on the very dissatisfied category. We're also given four possible choices as our answers. For choice A, we have 0.60, for choice B, we have 0.65. For choice C, we have 0.55, and for choice D, we have 0.50. So, we're asked to find the probability that a randomly selected employee from our sample is either satisfied or very satisfied. So we're going to begin by defining our events. So we're gonna say that event A is an employee that is very satisfied at their job. Event A is going to be very satisfied. And event B is gonna be an employee who just responded as being satisfied in their job. So those are gonna be our two events. And we're actually looking for the probability that an employee is either satisfied or very satisfied. So we're actually looking for the probability P of a union B. But here, A and B are mutually exclusive events, since you can't be very satisfied and satisfied at the same time. So recall for mutually exclusive events that when we look at the probability of the union of those events, that it's just gonna be equal to the sum of their individual probabilities. So, the probability of a union B is going to be equal to the probability of event A. Plus the probability of event B. So here we just need to determine the probabilities of each of our two events, event A and invent B. And we call that a probability is just gonna be the number of favorable outcomes divided by the total number of possible outcomes. So that means that our probability of a union B is going to be equal to or probability A of A. We're just going to have the number of people that responded as very satisfied, divided by the total number of people surveyed. So if you look at our chart here, we see that the number of people that responded very satisfied is 400. We'll have 400. That's going to be divided by the 1500, which is the total number of employees surveyed. Then we'll have plus or the probability of event B. That's gonna be the number of people that were satisfied in their job. And so if we look at our chart, we see that that is going to be 350. And then that gets divided by the total number of people surveyed, which is 1500. And so, when we evaluate this expression, we get that the probability of a union B is going to be equal to 0.50. And so that is the answer that we're looking for for this problem. And if we compare that to our answer choices, we see that the correct answer choice actually corresponds to answer choice D. So I hope that this explanation has been useful, and I'll see you in the next video.

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)
b. Randomly selecting a person from the sample who is conservative or very conservative

Key Concepts

Probability

Pareto Chart

Categorical Data

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