[NW] Selecting a Jury
The grade appeal process at a univ...

Question

[NW] Selecting a Jury

The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.

a. What is the probability of selecting a jury of all students?

Accepted Answer

Welcome back, everyone. In this problem, a panel of 4 is chosen at random from 15 male and 10 female applicants. What is the probability that exactly 2 of the selected are female? A says it's 1/5, B 157 divided by 517, C 189 divided by 506, and the D 117 divided by 489. Now, in this problem, if we're going to calculate this probability that we get exactly 2 of the selected applicants to be female, first we need to figure out how many different ways we can choose 4 applicants from the total number of applicants and then how many different ways we can choose 2 females from our 10 female applicants. So let's start with the total number of outcomes, the number of ways to select 4 applicants from 25. We can do that by using the combination formula. Recall, the combination formula basically says that. For and choose R, it's going to be equal to n factorial. Divided by r factorial multiplied by n minus r factorial. In this case, If we're calculating the total number of ways to select a panel of 4 applicants from 15 male and 10 female applicants or 25 applicants overall, then. In this case, n would be equal to 15 + 10, which is 25. And are the number we're choosing is 4, so we're looking for 25, choose 4, and by the formula that would be equal to 25 factorial divided by 4 factorial multiplied by 25 minus 4 or 21 factorial. That is gonna simplify it to 25 multiplied by 24, multiplied by 23, multiplied by 22, divided by the product of 432, and 1. And when we calculate here we should get that to be 12,650. In other words, there are 12,650 ways to select 4 applicants. From the planet. Or, or, yeah, 4 applicants from the total. OK, so this is our total number of outcomes. Now how many different ways can we select 2 female applicants from our 10 female applicants? Well, in this case, we need to calculate the number of ways to select exactly 2 females and 2 males. So if we think about it here, to select exactly 2 females. OK, because since we're selecting 4, if we select 2 females, then we would, we would have to be left with 2 males, right, on the other side. So to select exactly 2 females from the list from 10. Then that combination would be 10 choose 2 which equals. 10 factorial divided by 2 factorial multiplied by 8 factorial, and that would be equal to 45. Next to select. Exactly. Two meals. From the 15 male applicants, then that would be 15 choose 2, which equals 15 factorial divided by 2 factorial multiplied by 13 factorial that would be equal to 105. So the total number of favorable outcomes, let me put this on the right here, thus the total number. Are favorable outcomes. That is selecting two females and 2 males would be equal to 10 choose 2, 45, multiplied by 15 choose 2, 105, which equals 4,725 ways. So now that we have the number of total outcomes and the number of favorable outcomes, we can calculate the probability because now this means that the probability we select exactly 2 females, which means we'd have 2 males then. From our total list of applicants would be equal to 4,725 divided by 12,650. And when we simplify here, that leaves us with 189 divided by 506. This is the probability that exactly 2 of the selected applicants are female. If we look back at our answer choices, that means C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

[NW] Selecting a JuryThe grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.a. What is the probability of selecting a jury of all students?

Watch next

[NW] Selecting a Jury
The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.
a. What is the probability of selecting a jury of all students?