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Question 132 ptsA nurse from a hospital randomly selects people at the hospital waiting room until he finds a person who does not have a smart phone. Let , the prob...

Question

Question 132 ptsA nurse from a hospital randomly selects people at the hospital waiting room until he finds a person who does not have a smart phone. Let , the probability that he succeeds in finding such a person, equal 0.06.And, let denote the number of people he selects until he finds the person who has no smart phone: What is the probability that he must select more than 7 people before he finds one who has no smart phone? (up to four decimal places)

Question 13 2 pts A nurse from a hospital randomly selects people at the hospital waiting room until he finds a person who does not have a smart phone. Let , the probability that he succeeds in finding such a person, equal 0.06.And, let denote the number of people he selects until he finds the person who has no smart phone: What is the probability that he must select more than 7 people before he finds one who has no smart phone? (up to four decimal places)



Answers

Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Noah is planning his summer camping trip. He can’t decide among six campgrounds at the beach and twelve campgrounds in the mountains, so he will choose one campground at random. Find the probability that Noah will choose a campground at the beach.

All right So the probability that for a follow up interview we have all three are selected from hospital. Um that's gonna be 270 from the hospital Out of 953. And then we're just gonna subtract one each time. It's gonna have to 69 over 953 and 268 over 951. This one's supposed to be 952. Since we're reducing the population. We're not sad. We are not replacing. That's what I'm trying to say. And this turns out to be 0.2256 mm. And then for the next population what is the probability that all three are from the same hospital? Um So that's gonna be a couple different probabilities. Um we got 195 from one hospital and then we got 270 from another. Then we got 246 from the other And then 242. And each time they start at 953. Yeah. Yeah. Okay. And then we're just gonna multiply him by -1 and -2 each way. And each time we're going to subtract the population of the month. So the basic idea as we did last time it's gonna be our sample minus the number of times we've done this divided by the other the total population minds the number of times we've done this and we're gonna do this three times. So we're gonna be multiplying 12 terms and it's gonna come out to be 6%. Yeah.

Okay, because in this problem, we're told that 35% there's a 35% probability that a student is interested in protecting their online privacy and the problem as us to find the probability that had a four randomly selected students. What is the probability that none of them, zero of them want to protect their privacy? And so, in order to answer this question, we need to determine the probability of a person not wanting to protect their privacy. Well, the probability of a person interested in protecting their privacy is 35% or 0.35 So that means the probability of a person not interested in protecting their privacy is one minus 0.35 or 0.65 So this is the key, probably the key number that we need, because we know we want to find the probability that out of four randomly selected students, what is the probability of zero of them want to protect their privacy? So if we do that, we know we're going to multiply 0.35 to the zero of power. Because zero students wanted zero students want to protect their privacy and we're gonna multiply 0.65 times itself four times because all four of them do not want to protect their privacy. And that probability is your 40.65 And we also want to multiply by four choose for just so you guys. The reason why I'm writing it out like this is just so you guys get a general idea of what we're doing in the long term process because every problem that you solve in probability, you have to tackle with this mindset tackle with the mindset of how many people are interested in the event that you have the probability for how many people are not interested and the different arrangements that can occur. The reason why four choose war in this matter doesn't matter. That much is because the number of ways you choose four people out of a group of four people is just one way. So that means all of these students don't want to protect their privacy or none of them do. That means there's only one way, and if you evaluate this, the four choose four evaluates toe 10.35220 Power values to one. So you're just multiplying by 0.65 to the fourth power. Now, this could have been your first step. How? I just wanted to walk you guys through from the from this work use for times 0.35 to 0 with times 0.65 to the fourth down to this stuff. So if we solve points expired to the fourth power, you will get that. Our probability is zero is 0.1785 and that's our final answer.

This exercise. We reference back to exercise 17 which was the cell phone usage among teenagers. And we found that the probability that a randomly selected teenager owned a cell phone was 58% and we found them to be for newly trials because each teenager outcome was independent of the outcome for any other randomly selected teenager. And the outcomes possible for each teenager were either a success or failure, where we have defined success as that teenager having a cell phone. This time, we're as to consider a group of 20 randomly selected teenagers. And for part, they were asked to find the mean and standard deviation of the number of non smartphone owners in the group. So if we're part a less defined success as a teenager not owning a cell phone, therefore the probability of success is one minus 0.58 or a 0.42 and we can define X as the number of successes. So successes a teenager not having cell phone. So X is a binomial random variable based on 20 trials with probability of success of 0.42 So now, to find the mean and standard deviation. The expected value for the number of successes for a binomial random variable is given by N Times P. It comes out to 8.4. So in any randomly selected group of 20 teenagers, on average, we would expect 8.4 of them to be cell phone owners and the standard deviation for a binomial random variable. It's given by the square root of end times P Times Q. And this comes out to 2.21 So that's the standard deviation on the number of teenagers who do not own cellphones in groups of 20 and now for Part B, were asked for various probabilities on the number of people in this group of 20 uh, who own smartphones. So for Part B, it will be easier to define success as a teenager. Having a cell phone we're back to P is equal to 0.58 So now X is a binomial random variable based on 20 trials with probability of success of 0.58 Also, remember the probability mass function for a binomial random variable is given like this the probability that X is equal to K successes and so for the first part of part B were asked, What is the probability that they're not all smart phone owners? So this is the probability that X is less than 20 if we have less than 20 successes than they're not all cell phone users, and this can be equated to one minus the probability that X is equal to 20 and using our formula here and this comes out to zero point 99998 So we're almost certain that not all of them will have cell phones. And, of course, this would actually be a one minus here. Part two. We're. As for the probability, there are no more than 15 smartphones. So this is the probability that X is, at most 15 successes. If you were to calculate this manually, it would be easier to look at it as the probability that exes at least 16 because then you'd only have five terms to calculate using this formula. But for this problem, it's much easier to use software and using software. The value I got with zero point 965 so there's about a 96.5% chance that no more than 15 of teenagers in a group of 20 owns smartphones for Part three of Part B were asked the probability of exactly 10 of each. So that's 10 smartphone owners and 10 non smartphone owners. So this could be representatives the probability of exactly 10 smartphone owners. And this comes out to a probability of 0.136 and for part for we ask the probability that the majority don't have a smartphone. So let's define this. If at least half don't have a smartphone, then that is the majority. So this is the probability that X is less than or equal to 10 and this probability comes out to zero point 306

To find the probability of an event. We take the number of favorable outcomes and divided by the total number of outcomes. So in this problem, we're finding the probability that Donovan visits an out of state college if you randomly selects from 10 out of state colleges and foreign state colleges. So the number of favorable outcomes would be 10 because he has 10 out of state colleges on his list and the total number of outcomes would be 14. Because there are 14 colleges on his list altogether. Let's reduce that fraction, and we get 5/7 and that's the probability that he will visit and out of state college. And then we can convert that to a decimal. We're going to have to round it to three decimal places, and we get 30.714 as the probability of visiting and out of state college


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