winning-tickets-at-a-meeting-of-10-executives-7-women-and-3-men-two-door-prizes-are-awarded-find-the

Name: winning tickets at a meeting of 10 executives 7 women and 3 men two door prizes are awarded find the
Uploaded: 2020-09-23
Duration: 1 min 55 s
Channel: Numerade
Description: Winning Tickets At a meeting of 10 executives (7 women and 3 men), two door prizes are awarded. Find the probability that both prizes are won by men.

Question

Winning Tickets At a meeting of 10 executives (7 women and 3 men), two door prizes are awarded. Find the probability that both prizes are won by men.

Yixian Wang · Accepted Answer

So in this problem, we have seven women and three men, and there are two prizes. And we want to know the probability that both prizes go to men. Um, so in this problem, there is no order. So we don&#x27;t care about the order. And we use the combination in this problem. Um, so the probability the probability of two prizes won&#x27;t by men equals. So the numerator should be the number of ways to select two men out of three. So this should be three. Choose to on the denominator should be the total number of ways to choose to people out of 10. So this is 10 shoes took. And if you use a calculator for this, this is three divided by 45. Andi, this finally goes to thanks. 0.67

Noah Vigran · Answer

okay. And this problem, we are referring to a door prize. And if you do not know what that is, you kind of refer to my picture at the bottom. Uh, sorry for my lack of drawing skills. But basically, a door prize is similar to like a lottery. So it&#x27;s like when you enter and your ticket has a number on it and that same number goes into a bowl and then look, at the end of the night, they&#x27;re going to draw. In this instance, they&#x27;re gonna draw two tickets and then, like, the matching number would be the winner. And so this is very similar to drawing without replacement, because after you draw the first ticket, you have one less ticket in your total amount of tickets before you draw the second ticket. So in this case, we&#x27;re told that each member of the party has a your prize number per se, and we have 10 men at the event and 20 women making 30 total. So the problem wants us to know, wants us to find out the probability that both winners being both drawn ticket numbers are meant. And so I wrote this out here That would be the probability that the first was won by a man times the probability that the second was won by a man, given that the first was a man and this again kind of goes back to us, drawing without replacement. And so this would be the same as for the first being a man, we have 10 men over 30 total people because that&#x27;s just the probability that the first would be men times the probability that the second is a man, given that the first was also a man. So we have one last men like we won less man&#x27;s ticket in the door prize lottery. So we have nine and then also because we&#x27;re drawing without replacement per se, we have one less in the bullets wells and 9/29. And when you do this out, you have 0.10 24 or 10.24% would be our probability of this occurring

Ankit Gupta · Answer

since there are a number off, men&#x27;s is equal. Toby then and number off women&#x27;s is given Toby then. And so the total number off people is equal to 10 plus 10 their physical toe 20. Now we need toe find operability off, selecting two men and two women. No, this is equal. Toby, we need to select two men out off 10 and we need to select two women out off then Now we need to select four members out off 20. So by using the foam, love and see are such that NCR is equal to n factorial over r factorial multiplied with n minus r factorial we have This is equal toe 10 factorial over two Factorial multiplied with a factorial plus multiplied with 10 factorial over two Factorial multiplied with eight factorial Do I did by 20 Factorial divided by four Factorial multiplied with 16 factorial, so we&#x27;ll simply find it. We have 1 35 upon 3 23 So this is over on. So

Michael Wang · Answer

So we&#x27;re going to number 46. And it&#x27;s about a precedent of a look of a large company selecting six employees to receive a bonus. There are 19 women in 11 men. The probability that no woman is chosen. So that means that all men will be chosen. So a set of this problem by listening out the number of men and women. So they had 19 women and 11 men. So we arch finding the probability of that Colin man aren&#x27;t chosen. And to do so, we&#x27;re gonna have to think about these as six individual cases. So, um, doesn&#x27;t And they&#x27;re six, um, cases, sequential cases. So the first case is when the president chooses the first person and was the probability that they choose a man. It&#x27;s 11 out of 30. The next person that he chooses, the probability that he chooses another man will be 10 over 29. Okay, then it&#x27;s nine over 28. Look great. Over 27 seven over 26 and finally six over 25. Okay. And the reason why we subtract one from both the numerator and the dub and the denominator for each case that we go down is because, let&#x27;s just say in the first case we have chosen the first man. So in the power that we&#x27;re choosing from, um, there&#x27;s one less man in this one less person, So that&#x27;s why we reduce it by one each time. So if we use a calculator to simplify this, we&#x27;ll get the answer to be about seo 0.7

Ankit Gupta · Answer

that I 30 employees out off which 19 are women on 11 are men. We have to choose six employees to receive a special Boehner&#x27;s. The probability that no woman is chosen would be. Then all men are chosen. So choosing men, we have 11 C six choices upon 36 11 Victorian coupons. Expecto really into five factorial into party factorial six factorial into 24 pictorials. Expectorant except over cancels 11 factorial into 24 sectorial upon five factorial into tart effectively would be the answer.

James Chok · Answer

So what is the probability a person wins by picking seven of the correct numbers among seven numbers off the 1st 80 positive images? So if we imagine that walk worth 80 here, so if we imagine that 123456789 10 11 was the winning numbers, then we want to pick one True seven of these, so once again chooses a pick because in a lottery ordering doesn&#x27;t matter. So from the 11th from 11 we want true seven of them, and then this is your number off favorable outcomes. So the number of possible outcomes is from 81. Choose seven of them, and day seven of them are the ones that we picked. This is possible. So then the probability off when you is then 11. True seven. Divided by 80 shoes seven, which is 330. You bought it by 3,000,000,176 million 716,400 which is equal to three, divided by 28 million 879,000 2 40 which is equal to 1.39 times by 10 to the minus seven

Problem

Getting a Full House Find the probability of gett…

Problem 7 Easy Difficulty

Winning Tickets At a meeting of 10 executives (7 women and 3 men), two door prizes are awarded. Find the probability that both prizes are won by men.

Answer

$\dfrac{1}{15}$

Related Courses

Elementary Statistics a Step by Step Approach

Related Topics

Discussion

Top Intro Stats / AP Statistics Educators

Srikar K.

Megan C.

Heather Z.

Lucas E.

Intro Stats / AP Statistics Courses

Data And Variables

Data And Variables - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Allan G. Bluman

Elementary Statistics a Step by Step Approach

Srikar K.

Megan C.

Heather Z.

Lucas E.

Data And Variables

Data And Variables - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\dfrac{1}{15}$

Elementary Statistics a Step by Step Approach

Srikar K.

Megan C.

Heather Z.

Lucas E.

Data And Variables

Data And Variables - Example 1

Allan G. BlumanElementary Statistics a Step by Step Approach

Srikar K.

Megan C.

Heather Z.

Lucas E.

Allan G. Bluman

Elementary Statistics a Step by Step Approach