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Question

Educational Fellowship A university received 9 applications for three postdoctorate fellowships. Five of the applicants are men and four are women. Find these probabilities.
$$
\begin{array}{l}{	ext { a. All } 3 	ext { who are selected are men. }} \ {	ext { b. All } 3 	ext { who are selected are women. }} \ {	ext { c. Two men and one woman are selected. }} \ {	ext { d. Two women and one man are selected. }}\end{array}
$$

Yixian Wang · Accepted Answer

So in this problem we have five men and for women, Onda, we want toe randomly select three people Thio give them fellowships and we want to know the probability of the falling for situations. So let&#x27;s look at part A, um we want to know that all three fellowships the probability of all three fellowships go to men. Um, so those probability actually equals, um, the number of choices. We could have to select three people from five men, so the numerator would be five shoes three divided by the total number of choices. We could have to select three out of nine people. So the denominator would be nine shoes three. And the final result would be 0.11 night. Okay. And the next part we want to know all three. The probability of all three fellowships. Goto women. Um, similarly, the new murder should be the number of choices we could have Thio select three women out of four, so it should be four. Choose three and the same as above. Divided by 9 to 3. And the result goes to why no. 48 So the next part is a little bit different because we want toe first, select two men out of five, then select one woman out of four. So I have We&#x27;re going to do this and two step two steps. The first one should be five choose to times for choose one. So these are the the number of choices we could have to select two men out of five and then one woman out of four and divided by nine. Choose three. This is 10 times four. Divided by 84 Goes to point or 76 Okay. And finally, the last part. This is similar, um, with part C. First, we want to select two when women out of four, which should be for Jews to And then so that you are men out of five, which is five choose one divided by nine shoes. Three It goes to six times I&#x27;ve reminded by 84 and finally the result is point 357 and we&#x27;re done

Evelyn Cunningham · Answer

Let&#x27;s start with what we know in this particular problem, we have 10 people applying for a job, So we have 10 applicants. Of those 10 5 have college degrees and five don&#x27;t. And we are going to look at three applicants set random, and we&#x27;re going to focus on getting college graduates. So let&#x27;s look at what our probability distribution would look like. So when we look at these applicants and we select, we might end up with zero college grads, we might end up with one or two or three. Now, that&#x27;s the entire probability distribution. So the sum of our p of X column should equal one. Now, what are we trying to find when we actually higher? If the manager selects thes three applicants, we want the probability that all three were graduates. So we&#x27;re solely focused on this value right here. So our X value is three. Now, once we select a person to be the person that gets the job, we&#x27;re not gonna put them back into the pool of people. So therefore our sampling is done without replacement. So because of the sampling is done without replacement, we&#x27;re talking a about a hyper geometric distribution. And there&#x27;s a formula that governs hyper geometric distributions. And that formula reads the combination of a items taken exit a time multiplied by the combination of be items taken n minus X at a time all over a plus B items taken and at a time and a represents the count of favourable options. So in this case, we&#x27;re looking for college grads. So are a value is going to be five and b represents the unfavourable count. And in this case, we don&#x27;t want the ones with college degrees. So they&#x27;re the unfavourable. So be is going to take on a value of five. So we have all the information we have need to use this formula. We have an end value. We haven&#x27;t X value, even a value and a B value. So we&#x27;re ready to substitute in. So therefore, it would read the combination of five taken three at a time, multiplied by the combination of five taken the re minus three at a time all over five plus five combination taken three at a time. So now we can clean that up a little bit before we pick up our calculator. So it be five C three multiplied by five C zero all over 10. See three. And if you put that into your calculator, you will end up with a fraction that reads 10 for the numerator and 100 20 in the denominator, which reduces into 1 12 So the probability of getting three college grads when we select the applications at random would be one 12th. And if you want to do, you can put it into its decimal equivalent, which is approximately 0.83 and your answer would be 0.83 or window.

Victoria Dollar · Answer

Okay, So for this problem, we have 11 men. Um, I&#x27;m sorry. 11 women and nine men. So that&#x27;s a total of 20 people. And then we have a group of five people that I want to consist of two men and three women. So put females. So what I want to do is I want to go ahead and construct this so I&#x27;m in a creative fraction because it&#x27;s asking, um, find the probability that that committee will contain that. So what I want to do is I want to dio 20 Choose five is my total. And then I&#x27;m gonna have nine choose to for the men and 11 shoes. Three for the women. So this is going to be nine factorial over two factorial, seven factorial. And then I&#x27;m gonna have 11 factorial over three factorial. Um And then, of course, eight minus 11 Earths are 11 minus three is gonna be eight and then at the bottom of my have 20 factorial over five factorial, 15 factorial. So if I were to go ahead and just calculate all of this out mhm, then I will end up getting so I&#x27;m gonna end up getting 0.38313 is my final answer

Lourence Gonhovi · Answer

I believe that the committee contains three men and two women. So want to find the probability if we have court mine man and the live in three males, which gives us 20 people now we want to find the probability and that in this case we will have three men and two women market. So Ah, what? How do you select three men from Maine? Men? Nine Combination off three then and demeans not applied by combination off two women from 11. So it&#x27;s 11 seem to. And all this is divided by the sun. Most pits which is trained to survive, selecting five people from 20 and then this gear us little 0.298

Jake Zanazzi · Answer

you asked about selected, randomly chosen faculty members, the probability that you select a female or someone under the age of 40 giving people the probability selected. What&#x27;s the probability you like under 40? Really? Both of these things happen. This is going to be cool or clean. Since before females, 30 people total us. We&#x27;re five people who are under 30. And how many female 42 equal seven over 40. Now I e I think something over 40 minus the probably both gonna equal 9 13 us. How many people there over 42 6 Eat. I mean males air there Over 40 there. Six. So we have not was 8 to 17 by the 6 11

Michael Dunne · Answer

a mathematics faculty is composed of four females and nine males. Very important because now we know there are 13 total of the females to are under the age of 40. Of the males, three are under the age of 40. Before even go and read, the questions were being asked. I do want to organize their information. Let&#x27;s just put it into a table. We have male and female faculty, and we have just to age divisions we have under the age of forties. We&#x27;ll just call that less than 40. Um and then we just have the rest that are 40 year older. So greater than or equal to 40 Now it says, over the females to are under the age of 40 self tour under the age of 40 and there are four total. There must be two of the door, at least 40 for the males three or under the age of 40. Since there are nine males, there must be six that are at least 40. We know there are 13 total in this checks because we have three plus six is nine to into his four. That is our total of 13. We know that adds up. Now we want to find the probability that a a randomly selected faculty member is female or under the age of 40. Well, if we&#x27;re looking for a female or under the age of 40 females would be two and two or under the age of 40 could also include the three male faculty members that are under the age of 40. There&#x27;s a total of 34567 So for part A, we have a probability of seven out of 13 Part B. Do that one in blue. We&#x27;re looking for a male or over the age of 40 while for males there are nine of them, but also for looking for faculty over the age of 40. That would be, um, the two other females, which means three plus six is nine plus to Mars 11. So the probability of getting a faculty member that is either male or over the age of 40 would be 11 out of 13

Problem

Senate Partisanship The composition of the Senate…

Problem 3 Easy Difficulty

Answer

a.$\dfrac{5}{42}$b.$\dfrac{1}{21}$c.$\dfrac{10}{21}$d.$\dfrac{5}{14}$

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Allan G. Bluman

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a.$\dfrac{5}{42}$b.$\dfrac{1}{21}$c.$\dfrac{10}{21}$d.$\dfrac{5}{14}$

Elementary Statistics a Step by Step Approach

Boris M.

Megan C.

Monique R.

Heather Z.

Data And Variables

Data And Variables - Example 1

Allan G. BlumanElementary Statistics a Step by Step Approach

Boris M.

Megan C.

Monique R.

Heather Z.

Allan G. Bluman

Elementary Statistics a Step by Step Approach