In Exercises 1–10, use the data in the accompanying table and ...

Question

In Exercises 1–10, use the data in the accompanying table and express all results in decimal form. (The data are from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519.)

Complement If L represents the event of randomly selecting one of the study subjects and getting someone who writes with their left hand, what does L represent? Find the value of P(L)

Accepted Answer

Below 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. In a survey about preferred types of devices, people were asked whether they prefer touchscreen devices or keypad-based devices. The results are shown below. So we have a table where the far right column states prefers keypad. And then on the left column we have prefers touch screen, and then on the far left column we have students and professionals. So students who prefer touch screens are 44, and students who prefer keypad is 106, Professionals who prefer touch screen are 36, and professionals who prefer keypads are 64. Let T capital T represent the event of randomly selecting a person who prefers a touchscreen device. What does T bar represent? Find the value of capital P of T bar. Awesome. So it appears for this particular problem we're asked to solve for two separate answers. Our first answers we're trying to determine what the value of T bar represents, and then our second answer we're ultimately trying to solve for is we're trying to determine or find the value of the probability of T bar, so P of T bar. So with that said, now that we know what we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is T bar is the event of preferring touch screen. P of T bar is equal to 0.68. B is T bar is the event of not preferring touch screen. Which is P of T bar is equal to 0.68, C is T bar is the event of preferring touch screen. P of T bar is equal to 0.32, and finally, D is T bar is the event of not preferring touch screen. P of T bar is equal to 0.32. Awesome. So it appears for this particular problem, we need to first focus our attention on the interpretation of what Tar means. What does this Tar mean? So we need to note and recall for this particular problem T bar will represent the event of randomly selecting a person who does not prefer a touch screen device, meaning they prefer to use keypad-based devices. So, let's make a note of that. So T bar. Is equal to, so someone who does not prefer. Touch screen. So I'm gonna shorten it up. So D and PTS, so does not prefer touch screens. Awesome. So that will mean that P of T bar. is going to be equal to the probability, which is denoted as P, so the probability that the selected user does not prefer touch screens. So P of T bar means that it's the probability that they do not prefer touch screens. Awesome. So now we need to switch our attention to focus on the total number of people surveyed, so we need to take 44. Plus 106 + 36 plus 64. Once again we received all of these values from our table that's provided to us by the problem itself. So when we add 44, 106, 36, and 64, we will find that it's equal to 250 people. So, now we need to determine the number of people who prefer touchscreen devices, so we'll call this event T. So focusing on event T now, we need to take 44 + 36 because we have students, which are 44 students prefer touch screens, and we have 36 professionals who prefer touch screens, which will give us a total of 80. Fantastic. And once again. Oh, so we don't get confused, we'll call it ET so event T, and then 250, let's make a note that this is the total number of people that participated in this survey. Fantastic. So moving right along here. So now, our next step is we need to determine the number of people who do not prefer touchscreen devices. So this is event T bar. So event Tar states that we know that there's a total of 250 people who participated in this particular survey, and we need to note that. The event that actually preferred touch screens was 80, so we need to subtract 80 from 250, so when we take 250 and we subtract 80, we will find that it's equal to 170. So that means that we can solve for a P of T bar now. So P of T bar is going to be equal to 170, is there's we discovered that there's 170 individuals who participated in this particular survey. That do not prefer to use, that do not prefer using touch screens, so we need to take 170, and we need to divide it by the total number of outcomes, which is 250, so 170 divided by 250. When we plug that into our calculator, we will find that it's equal to 0.68, and that's it. That is one of our final answers. Hooray, we did it. So therefore, without a doubt, Tar represents the event that the selected person or user does not prefer to use a touch screen device. And the value of P of T bar is equal to 0.68. So that means without a doubt, our final answer has to be multiple choice answer letter B, which states that T bar is the event of not preferring touch screen, and P of T bar is equal to 0.68. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Probability

Complement of an Event

Data Representation

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