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)

a. Find the probability that a randomly selected bachelor's degree-earning student is male, given that the degree is in business.

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 gonna 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 graduate with degrees in science and non-science fields. Male, female, science. 75,000, 95,000, non-science, 105,000, 125,000. What is the probability that a randomly selected science graduate is male? Awesome. So it appears for this particular prom we're ultimately trying to determine what is the probability value that a randomly selected science graduate is male based on this information that is given 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 0.441, B is 0.500, C is 0.560, and D is 0.395. Awesome. So before we start solving for this problem, let's take a moment to take our statement that we're asked to solve for. So let's let's write mathematically how to write the probability that a randomly selected science graduate is male. So taking that statement and writing it into a mathematical statement, we can state that the probability. Of male, which I'll just denote as M. Given science, which we'll call S for short. So writing this as a mathematical statement, so we're saying the probability that a randomly selected science graduate is male, so we're saying the probability. So P parenthesis M S. So once again, this is the probability of male given science. So this is the probability that a that a randomly selected science graduate is male. So, with that in mind, our first step that we need to take in order to solve this problem is we need to identify the number of males who received a science degree, which according to our table is 75,000. Our second step now is we need to identify the total number of science graduates, so we need to take 75,000 plus 95,000, which is equal to 170,000. Fantastic. Moving right along here. So now, our next step. Which is our 3rd step. we need to compute the conditional probability, meaning we're solving for P M S, so meaning we need to take P M S, so we're solving for the probability that a randomly selected science graduate is male. So this will be equal to 75,000 divided by 170,000. Which, when we plug this into our calculator and we round to approximately 3 decimal places, because all of our multiple choice answers are rounded to 3 decimal places, you will find that this will be approximately equal to 0.441, and that is our final answer. Hooray, we did it. So therefore, without a doubt, The probability is approximately 0.441, or we can also write this as a percent, 44.1%. But since all of our multiple choice answers are written as decimals, we do not have to write it as a percentage. So that means our final answer without a doubt has to be multiple choice answer letter A, which once again is 0.441. 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

Total Probability

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