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.

7. Business Degrees The table shows the numbers of male and female students in the United States who received bachelor's degrees in business and nonbusiness fields in a recent year. (Source: National Center for Educational Statistics)

b. Find the probability that a randomly selected bachelor's degree-earning student received a business degree, given that the student is female.

Table showing the number of male and female students earning business and nonbusiness bachelor's degrees in the U.S.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A college tracks the number of male and female students who received a bachelor's degree in science and non-science fields in a given year. Male, female, science, 32,800. 41,600 non-science, 67,500, 80,900. What is the probability that a randomly selected bachelor's degree recipient earned a science degree, given that the student is male? Awesome. So it appears for this particular problem, we're ultimately trying to determine the probability that a randomly selected bachelor's degree recipient earned a science degree, given that that student is male based on the information that is provided to us by the prom itself. So with that in mind, now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is 0.298, B is 0.327, C is 0.382, and D is 0.421. Awesome. And our first step that we need to take is we need to identify the number of male students who received a science degree, which is 32,800. Our second step that we need to take is we need to identify the total number of male students, which is 32,800 plus 67,500. Which is equal to when we add these two values together, 100,300. Awesome. So now, our 3rd step is we need to calculate the conditional probability. Which ultimately we're trying to solve for the probability that a randomly selected bachelor's degree recipient earned a science degree given that the student is male. We could write this as a mathematical statement that states that P of S given, so probability that the probability of science. Given male, which I'll call S for science, male is just gonna call M for short. So once again, this is the probability that a randomly selected student has a bachelor's degree with a science major, given that the student is male. So we could write this as P S M. And this is equal to 32,800. Divided by 100,300, and when we plug in this expression into our calculator and we round to three decimal places, because as you can see all of our multiple choice answers are rounded to 3 decimal places, we will find that this is approximately equal to 0.327. And that is it. That is our final answer. Hooray, we did it. So therefore, the probability is approximately 0.327, and this corresponds to multiple choice answer letter B, which once again is 0.327. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Conditional Probability

Joint Probability

Marginal Probability

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