Finding Conditional Probabilities In Exercises 7 and 8, use th...

Question

Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.

8. Retirement Savings The table shows the results of a survey in which 250 male and 250 female workers ages 25 to 64 were asked if they contribute to a retirement savings plan at

work.

b. Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work.

Table displaying survey results of 500 workers on retirement savings contributions by gender.

Accepted Answer

Welcome back, everyone. A company surveyed 180 engineers and 220 designers about whether they use standing desks at work. The results showed that 90 engineers and 60 designers use standing desks. What is the probability that a randomly selected standing desk user is a designer? A says 2 divided by 5. B 2 divided by 8. C 2 divided by 3 and D 4 divided by 7. So for this problem, let's define an event A. We're interested in the probability that a randomly selected standing desk user is a designer, so we can say that A represents a probability of designer. Given Standing Desk user. So what we want to do is simply recall that the probability of A is the ratio of two numbers, M and N. M is the number of favorable outcomes, and N is the total number of outcomes. So let's begin by finding N, the total number of outcomes, and since we're given. That our user is a standing desk user and is simply the total number of standing desk users. So we have 90 engineers and 60 designers who use standing desks. So we are going to add 90 plus 60, which gives us 150, right? And now M is the number of favorable outcomes we're looking for a designer, and we're given 60 designers. So now we are ready to identify the probability of A as the ratio between 60 and 150, right? dividing the two numbers, we get 2 divided by 5 because both the numerator and the denominator are divisible by 30. Meaning the correct answer to this problem corresponds to the answer choice a. Thank you for watching.

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