Question

A quiz consists of 6 True/False questions. Assume that the questions are independent. Also, True and False are equally likely outcomes when guessing the answer to any question.

What is the probability that a student guesses each question correctly. Round your answer to 3 decimal places.

Answer 1

Answer:

Guessing A quick quiz consists of a true/false question followed by a multiple-choice question with four possible answers . An unprepared student makes random guesses for both answer. a. Consider the event of being correct with the first guess and the event of being correct with the second guess. Are those two events independent? b. What is the probability that both answers are correct? c. Based on the results, does guessing appear to be a good strategy?

Video Transcript

in Problem 21 we will discuss the concept of guessing for a quick West. Here we have a quick with the consistency of two questions. The first question question A consists of a true or false question. True or falls. The second question be consists of multiple choice, and we have four possible answers. B, me, C and D. And of course, there is only one correct answer for unprepared student who will get the answers for questions. E. And the question be, You want to give some statistics about this guy for birdie? Considering the event of being correct with the first I guess, then the probability of a where is being correct and the probability of being correct for the second question, then the probability of B is the probability of being correct. Four question. Are those two events independent? Of course, these two events or independent the occurrence of one does not affect the other for birth. We What is the probability that both answers are correct? This means we need to get the probability of a Intersect B. And because these events are independent, as we've answered in barta, the probability of the intersection would be the probability of a want to blow it by the probability of people, we can think of this problem as to individual experiments. This is the first experiment then this is the second experiment, and the probability is the multiplication. Oh, the experience, The probability of being correct for A is just to get the true answer. We have only two answers. We will choose one of them. Then the probability is both the ability to get through from Truell forces one divided by two half and the probability of being correct. For example, if we have the correct answer, is it, then we will choose one out of four. Then the probability of being correct to choose a is one out of four. Then the answer is one divided by it or we can write it in percentage. It's 12.5% for birth C. We want to see what is the guessing. Guessing, of course, appears to be not good, because to get a full mark, the quick quiz, the quick quiz you have, you have only 12.5% probability for this. And of course, this value is very low to make a guess on it. And this is the final answers of our problem.

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Answer 2

Given: A quiz consists of 6 True/False questions. Assume that the questions are independent. Also, True and False are equally likely outcomes when guessing the answer to any question.

To find: Probability that a student guesses each question correctly

Solution: For finding the solution, we need to use the binomial probability which is used for finding the probability of r successes when an experiment is done for n times and only 2 possible outcomes are there.

Here, true and false are the only options. The number of questions is 6.

Therefore, n= 6

Let answering the answer correctly be a success and not answering it be a failure.

It states that a student corrects all answers. Therefore, number of success (r) = 6

Since the answer can only be false or true, the probability of both success and failure is 1/2.

Therefore, probability of success (p) = 1/2

Probability of failure (q) = 1/2

The mathematical form of binomial probability is:

$\binom{n}{r} {p}^{r} {q}^{n - r}$

Using the values:

$\binom{6}{6} { \frac{1}{2} }^{6} { \frac{1}{2} }^{6 - 6}$

$= \binom{6}{6} { \frac{1}{2} }^{6} { \frac{1}{2} }^{0}$

$= \frac{1}{64}$

since

$\binom{6}{6} = 1$

1/64 rounded to three decimal places is equal to 0.016

Therefore, the probability that a student answers each question correctly is 0.016.