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Suppose that a person takes a 10 question true or false test andguesses the answers. find the probabilty of getting at most 4answers correct...

Question

Suppose that a person takes a 10 question true or false test andguesses the answers. find the probabilty of getting at most 4answers correct

suppose that a person takes a 10 question true or false test and guesses the answers. find the probabilty of getting at most 4 answers correct



Answers

Guessing on a Test An exam has ten true-false questions. A
student who has not studied answers all ten questions by just
guessing. Find the probability that the student correctly
answers all ten questions.

When a student is guessing the answer can be either correct or incorrect. So probably be off is equal to one by do, which is equal to probably be off in good. We have to find the probability that the student correctly answers all 10 questions correctly, answers all 10 equations. This would be one for me to be part 10 because I will do one of 110

In Problem 32. We have a student who takes a quiz, which consists of the 10 questions through all force, then question. True or false, the student guesses all the answers. Then we want to calculate the probability that the students answers exactly one question correctly, which means you get one out of 10 in this course. Let's it's translate this statement through all force. True force means there is a probability of 50% to answer each question. Correct, because it's true or false. If he gets a true, then there is a 50% chance to get the answer is true, but we have another thing. Questions. This means we have a problem, and we can define a random variable X, which follows a binomial distribution within equal. Stine have then trials, and the success probability equals 4.5 p equals 0.5. Because this is a true or false question, the probability to success or the success probability of the success rate equals 4.5. The probability to answer one question, correct then out of them, which means we want to calculate the probability of X equals one out of 10. What is the probability that the student answers exactly one question, which means X equals exactly one it equals and let's go. Let's write the equation of the formula and I at the Blood Boy Success Probability to the bar of I multiplied by one minus. B was about minus soy equals and is given by 10. Are you is selected by one. Only one question deployed by B. We have concluded that B equals 0.5. There's a lot of one deployed by one minus B, which is also a 10.5. It's about of n minus one. She is nine. These equals Oh point Oh, mine It or in percentage approximately equals 1% Then the probability to have only one correct question out of the 10 questions backwards 1%.

All right. So we've got ourselves another binomial distribution problem here. It's asking us again if we take a five question. True false quiz. What is the probability? Where the chances that we could get exactly four. Correct, if we guess on every problem. Okay, so, just like before, this is our binomial distribution again. This is a review from 12-8. So you should have already seen this. If you haven't seen this thing, you should back up and go through the actual section because it's not meant to be you learning it for the first time. This supposed be reviewing. So it's assumed that you've already seen this binomial distribution before. Okay, so we know there's four variables that we need to be able to, um, plug everything in to actually solve out this formula. We need the number of total trials. We need the number of successes that we're looking for. We need the probability that we will get a success on any given trial and the probability that we will fail on any given trial. Okay, well, we've been told this is a five question test, right? So that is five different trials. Five separate questions that we have a chance to get right. We are being asked specifically on this question the probability of us getting exactly four correct. So that's the number of successes that we want. We want four successes. Okay, so now the question is what is the probability on either on any question that we will succeed versus the probability on any question that we will fail? That's the nice part about this. Question is, it's very straightforward because it's a true false test. There's only two options. So every question when we take a guess, we have a 50 50 shot that we're going to get it right. Meaning there is a one in the wrong color. There is a one in two chance that we will get it right and there is a one in two chance that we will get it wrong because there's two possible answers. We either pick true or re pick false, and one of them is right. One of them is wrong, so one out of two chance for each of them. Okay, as long as we understand all of that, the rest of this is just plugging into the formula, plugging it into our calculator and we should be done. So if we plug it into the formula up there, we've got P of X equals the combination of five hopes change the color combination of five comma four. So five choosing four times the probability of success which is 1/2 being taken to the power of how many successes we want, which we wanted four successes. Then we have to multiply that by the probability that we will fail, which is also 1/2 1 out of two. But that is being taken to the power of our number of trials minus our number of successes, which would be five minus four. Now, if you go to your calculator, you should have a button somewhere that looks something like this, and that should allow you to do combinations. Hopefully, you've already found that cause again, the ideas. You've already done this section before, So you should have already had to plug into your calculator like this before. Might have to be in a menu, But you should able to find that button somewhere. So that will allow you to do five choose for which should give you five. Then we've got 1/2 to the fourth, Power one after the fourth. Power is 1/16 because one of the fourth is one and to the 4th 2 times two is 44 times to his 88 times two is 16. All right, five minus four. For that, exponents would give us 1/2 to the first power. Anything to the first power is just itself. Meaning we've got five, which maybe we should really write as a fraction since everything else is a fraction. So remember, any whole number can be expressed as a fraction by putting it over one. So we'll just write. Five is 5/1 times 1/16. Was it really bad? Six and 1/2 to the first. Power is just 1/2. So now we just need to multiply all of these together and we've got our answer. Remember, when you are multiplying fractions, you just multiply. All the numerator is together. Multiply all the denominators together. So five times one times one, his five one time 16 times to would be 32. Meaning that our chances of getting four out of the five questions on a true false test correct if we guess, is five out of 32

Question says that you're gonna have 10 true and false questions on a past, and the student answers them all by guessing. And the first part of the question says, What's the probability that you get all correct? So if you think about that, there are 10 questions. Um, there are two answers per question. So if you think about that total number of possible answers, then our is 20 There. It's not 20. It's to to the 10 because you've got two possibilities each time. And then there's only one way to get them all right. There are two and is 1000 4 And so that would buy and E says find, probably getting athletes seven. So you'd have 1000 and 24 possibilities and and you have to have and seven of the. So if I just figure out what 10 June 7 is, I'm just gonna grab 120. Different possibilities are different ways to get seven right, so you have 120 divided. By that 10th 24 it was just 15 and a 128. Or if you want the approximate valuable 11 well, 12%. So that's my answer for pardon. Be


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