the-table-shows-the-number-of-cities-in-a-region-of-the-us-that-are-served-by-the-given-number-of-ai

Question

The table shows the number of cities in a region of the U.S. that are served by the given number of airlines. Use the table for Exercises $21-22$ .
What is the probability that a city chosen at random is served by exactly 4 airlines?
$$
\begin{array}{llll}{	ext { A. } \frac{1}{18}} & {	ext { B. } \frac{4}{21}} & {	ext { C. } \frac{2}{11}} & {	ext { D. } \frac{2}{9}}\end{array}
$$

Tony Wilson · Accepted Answer

So we want to use that table to find the probability that a city change in at random is served by exactly four airlines. So the first thing you have to do is find the total of the right hand column. So the total is 99 and then four said 18 number of cities, so 18 over 99 would reduce to two over 11 and that answer then would be C.

Martha Richards · Answer

So when you look at the table that they provide, you see that they have the number of airlines, one through sex and the number of cities, and those are listed there in the table. And the question is asking, What&#x27;s the probability? What&#x27;s the probability that they&#x27;ll have that this If you pick some city a random that was provided there? What&#x27;s the probability that it will have at least at least one airline at that city? And because all that includes all of them, then that means just the total number over the total number, which is, if you have the same number divided by the same number, that probability is equal to one, so that would be answer choice, Jay.

Joshua Argo · Answer

today. We&#x27;re gonna be looking at the probability um having to do with airlines overbooking flights, meaning that they sell more seats than they&#x27;re actually available. Banking on the fact that some passengers will not show up. And we know that that is definitely possible and we know the airlines do that because they are interested in making money. Um So in this particular instance we have 50 seats on the plane and there are 55 tickets that are sold. And then we have a probability um distribution given with the probability of a certain number of passengers actually showing up. So part A. We are looking what is the probability that the flight will accommodated accommodate all passing all ticket ticketed passengers who show up and that&#x27;s going to be based off of our probability distribution. The probability that are variables wa Wise 45 plus the probability that Y is 46 all the way up to the probability That wise 50 because of 46 passengers show up. There&#x27;s enough seats for everybody. If 45 passengers show up, there&#x27;s enough for everybody all the way up to 50. And we&#x27;re just gonna take those probabilities from our distribution and add those up just and that will give us our answer for um or a Which is a pretty high percentage. Okay, it&#x27;s 83%. So 83% of the time their lines find they don&#x27;t have to give out any vouchers. They don&#x27;t have to try to make it right with anybody. Everything&#x27;s good. Okay. The passengers showed up. There was a spot for him on the plane. So then part B. It says what&#x27;s the probability that not all ticketed passengers who show it can be accommodated. Which we could take the probability that 51 show up and add it all the way to 55. Um I&#x27;m also just going to assume based off of our answer of a that this is all possible outcomes. There&#x27;s never been a chance of 44 passengers show up or anything less than that. So always at least 45 show up. I&#x27;m gonna assume that this probability distribution adds up to one. So in that case we can just take our probability from part a and subtract it and that gives us that there&#x27;s a 17% chance that there&#x27;s some um that there&#x27;s at least gonna be one extra passenger show up that they have to accommodate for give them a travel voucher et cetera. Um And of course we know that the profit function that we&#x27;re looking at here for those for those airlines is still in their favor. And uh then for part C if you&#x27;re the first person on the standby list, so that means that you need just one seat, at least one seat open. Okay? So in that case you&#x27;re looking for the probability that Y is less than or equal to 49, you need at least one seat. All right, so in that case 49 passengers show up, you&#x27;re able to get on the plane, 48 shows up, you and the person behind you were able to get on the plane. So, from our probability distribution, we&#x27;re going to add up the probabilities all the way um To that all the way up to 49 passengers. Which is a pretty strong possibility. Okay, there&#x27;s a 66% chance that you&#x27;re gonna be able to get on the plane if you&#x27;re on the first standby list and then the second part of part C. What is the probability if you&#x27;re the third person? So that means you need at least three seats. All right. So you could be 47th um In line actually 40 08:48 49 50 Um to have three seats if you&#x27;re um No, I take that back. It is 47. Um You&#x27;re 3rd person in line. You would Need three seats there, so 0.5 plus 0.10 plus 0.12. And you have a 27% chance if you&#x27;re a third person in line

Kerry Thornton-Genova · Answer

we&#x27;re being asked to some the probabilities that are answers to problems 40 through 44 problem 40. We were asked to find the probability that all four survived, and we found that it was 1/16 in Problem 41. We were asked to find the probability that only one survived. We&#x27;ve found that that was four out of 16 or 1/4 in Problem 42 were asked to find the probability that exactly to survive. We found that probability to be 6/16 or three X in problem 43 were asked to find the probability that four survived. We&#x27;ve found that this was four out of 16 or 1/4 problem. 44 were asked to find the probability that none survived. And we found that this was 1/16. Yeah, that&#x27;s what way will be totaling 1/16 Those 4/16 plus 6/16 plus 4/16. Yeah, plus 1/16 right. When you&#x27;re doing addition of fractions, you total across the top and keep the denominator the same. If it is identical, since all are over 16 we know that this will be over 16 and all we have to do is total the numbers in the numerator one plus four plus six plus four plus one is 16. That means our probability is 16/16 or one. This should make sense because this corresponds with 100% probability. We have thus covered all of the scenarios, which means that one of the scenarios must occur, making the some of them 100%.

Eric Wendland · Answer

So in this example, we have four algebra books, three literature books to bio books. So we have nine books total. And then we&#x27;re asked to find the probability of selecting an algebra or a literature books. So the first thing we&#x27;re asked to do is answer of these are mutually exclusive or inclusive. Since we know that you can&#x27;t select both in algebra and a literature book at the same time, we know they&#x27;re mutually exclusive. You only can choose one book, and we know that&#x27;s either an algebra or literature books sense. Now we&#x27;re asked to find the probability of selecting algebra and literature books, and we now they&#x27;re mutually exclusive. We could just add the probabilities. You know, there&#x27;s four algebra books out of a total of nine and three literature books out of a total of nine. So the probability of selecting an algebra literature books would just be adding to together, which would be seven nights

Lourence Gonhovi · Answer

So the probability expressed in simplified faction that the randomly selected American edged 25 for above not completed four years off college is now. You can take a reference to the diagram keeping question. Uh, now you can see that to wic whole. The numbers that you guys off high school. They&#x27;re less than four years off my school and already complained a lot off working. So the best way to do it is just to find those we have completed before year, Uh, college, and then some clicked show. Mom, I want to get the compliment, and that will be our ask. So So the probability Oh, uh, greater than four years is equal to one minus. Now we look att, the probability off Those were finished college program, which is four years or great in the 40 five in total, divided by the torta for the experiment or the sample space, which is under the 74. So if you subtract one minus 45 4 from 74 you will get 129 divided by 1 74 and you can divide by three three into 12. It caused four times three into line because three times playing into 17 It caused five times is, uh, remained off too. Three into train before that age, so simplified the hands off the 43 divided by 58.

Problem

The table shows the number of cities in a region …

Problem 21 Medium Difficulty

Answer

$\frac{2}{11}$

Related Courses

Algebra

Related Topics

Discussion

Top Geometry Educators

Christine G.

Heather Z.

Kristen K.

Michael D.

Geometry Courses

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

Recommended Videos

Watch More Solved Questions in Chapter 12

Video Transcript

Prentice Hall, Basia Kennedy, Dan Ramirez

Algebra

Christine G.

Heather Z.

Kristen K.

Michael D.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{2}{11}$

Algebra

Christine G.

Heather Z.

Kristen K.

Michael D.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

Prentice Hall, Basia Kennedy, Dan RamirezAlgebra

Christine G.

Heather Z.

Kristen K.

Michael D.

Prentice Hall, Basia Kennedy, Dan Ramirez

Algebra