Edward has to take a five question multiple-choice quiz and

Shelia Lawrence 2021-12-19 Answered
Edward has to take a five question multiple-choice quiz and his socialolgy class. each question asked four choices for answers of which only one is correct. assuming that edwards guesses on all five questions. what is the probability that he will answer a) all five questions correctly b) exactly 2 questions correctly c) at least two questions correctly

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

habbocowji
Answered 2021-12-20 Author has 5625 answers
Step 1
Given,
Total number of questions \(\displaystyle={5}\)
Probability of success \(\displaystyle={\frac{{{1}}}{{{4}}}}\) ( since each question has only 1 correct choice out of 4 choices)
We use binomial distribution here.
Step 2
(a) The probability that he will answer all five questions correctly:
\(\displaystyle{P}{\left({X}={5}\right)}={5}{C}_{{{5}}}{\left({\frac{{{1}}}{{{4}}}}\right)}^{{{5}}}{\left({1}-{\frac{{{1}}}{{{4}}}}\right)}^{{{5}-{5}}}\)
\(\displaystyle={0.000977}\)
(b) The probability that he will answer exactly 2 questions correctly:
\(\displaystyle{P}{\left({X}={2}\right)}=^{{{5}}}{C}_{{{2}}}{\left({\frac{{{1}}}{{{4}}}}\right)}^{{{2}}}{\left({1}-{\frac{{{1}}}{{{4}}}}\right)}^{{{5}-{2}}}\)
\(\displaystyle={0.26367}\)
(c) The probability that he will answer at least 2 questions correctly:
\(\displaystyle{P}{\left({X}\geq{2}\right)}={1}-{P}{\left({X}{ < }{2}\right)}\)
\(\displaystyle={1}-{P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}\)
\(\displaystyle={1}-{\left[{0.2373}+{0.3955}\right]}\)
\(\displaystyle={1}-{0.6328}\)
\(\displaystyle={0.3672}\)
Not exactly what you’re looking for?
Ask My Question
0
 
autormtak0w
Answered 2021-12-21 Author has 508 answers

Step 1
a) The probability that Edward will answer all the six questions correctly is,
\(P\text{(Six correct answers)}=((6),(6))(\frac{1}{4})^{6}(\frac{3}{4})^{0}\)
\(\displaystyle\approx{0.0002}\)

Step 2
Thus, the probability that Edward will answer all the six questions correctly is 0.0002.
b) The probability that Edward will answer exactly two questions correctly is,
\(\displaystyle{P}\text{(Two correct answers)}={\left(\begin{array}{c} {6}\\{2}\end{array}\right)}{\left({\frac{{{1}}}{{{4}}}}\right)}^{{{2}}}{\left({\frac{{{3}}}{{{4}}}}\right)}^{{{4}}}\)
\(\displaystyle\approx{0.2966}\)
Step 3
Thus, the probability that Edward will answer exactly two questions correctly is 0.2966.
c) The probability that Edward will answer at least two questions correctly is,
\(\displaystyle{P}\text{(At least two correct answers)}={P}{\left({X}\geq{2}\right)}\)
\(\displaystyle={1}-{P}{\left({X}{ < }{2}\right)}\)
\(\displaystyle={1}-{P}{\left({X}\le{1}\right)}\)
\(\displaystyle={1}-{\left[{P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}\right]}\)
\(\displaystyle={1}-{\left({0.1780}+{0.3560}\right)}\)
\(\displaystyle={0.4660}\)
Thus, the probability that Edward will answer at least two questions correctly is 0.4660.

0
nick1337
Answered 2021-12-28 Author has 10160 answers
I think the answer is c, at least three questions are correct, because he cannot answer everything correctly, and he cannot get the perfect number, 3.
0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-27
On a 8 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
asked 2021-10-01
Suppose that you are taking a multiple-choice exam with five questions, each have five choices, and one of them is correct. Because you have no more time left, you cannot read the question and you decide to select your choices at random for each question. Assuming this is a binomial experiment, calculate the binomial probability of obtaining exactly one correct answer.
asked 2021-12-17
Beth is taking an eleven​-question ​multiple-choice test for which each question has three answer​ choices, only one of which is correct. Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or​ 2, the second if the die shows 3 or​ 4, and the third if the die shows 5 or 6. Find the probability of the stated event.
exactly
four
correct answers
asked 2021-09-03
A literature professor decides to give a 10-question true - false quiz to determine who has read an assigned novel.
If a student who read the novel has a chance 90% of answering a question correctly, what is the chance of that student scoring 8 or more questions correctly?
asked 2021-09-24
A Finite final consists of 50 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 45 or better) by purely guessing on each question.
asked 2021-09-20
You took a test with 40 multiple choice questions. Each question had 5 choices. What is the probability that you get at least 28 questions correct if you guessed in all of them.
asked 2021-10-01
Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are \(\displaystyle{n}={8}\) trials, each with probability of success (correct) given by \(\displaystyle{p}={0.20}\). Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 3.

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question
...