Question

Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has...

Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.)

(a) What is the probability that he will answer all questions correctly?


(b) What is the probability that he will answer all questions incorrectly?


(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.


Then use the fact that P(r ? 1) = 1 ? P(r = 0).


Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?

They should be equal, but may not be due to table error.They should not be equal, but are equal.    They should be equal, but may differ slightly due to rounding error.They should be equal, but differ substantially.


(d) What is the probability that Richard will answer at least half the questions correctly?

Homework Answers

Answer #1

a)

probability that he will answer all questions correctly=(1/5)4 =0.002

b)

probability that he will answer all questions incorrectly =(4/5)4 =0.410

c)

probability that he will answer at least one of the questions correctly =1-0.410 =0.590

They should be equal, but may differ slightly due to rounding error.

d)probability that Richard will answer at least half the questions correctly =P(X>=2)=

=0.181

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has...
Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions...
Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has...
Richard has just been given a 4-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all four questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions...
Richard has just been given a 6-question multiple-choice quiz in his history class. Each question has...
Richard has just been given a 6-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all six questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions...
Richard has just been given a 6-question multiple-choice quiz in his history class. Each question has...
Richard has just been given a 6-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all six questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions...
Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has...
Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, find the indicated probabilities. (Round your answers to three decimal places.) (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions...
Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has...
Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all ten questions, find the indicated probabilities. (Round your answers to three decimal places.) What is the probability that Richard will answer at least half the questions correctly?
Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three...
Richard has been given a 5-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 5 questions, find the probability that he will answer at least 4 questions correctly. Round your answer to the nearest thousandth.
A student has just been given a 10-question multiple-choice quiz. Each question has five answers, of...
A student has just been given a 10-question multiple-choice quiz. Each question has five answers, of which only one is correct. The student has not attended class recently, and doesn't know any of the answers. Assume that guesses are made on all ten questions, find the indicated probability. (Round your answer to three decimal places.) What is the probability that the student will answer all questions incorrectly?
a) A student has just been given a 7-question multiple-choice quiz in their anatomy class. Each...
a) A student has just been given a 7-question multiple-choice quiz in their anatomy class. Each question has five answers, of which only one is correct. Since this student has not attended any classes recently, they do not know any of the answers and must guess on all 7 questions. What is the probability they will get at least one question correct? a. 0.7903 b. 0.8154 c. 0.3670 d. 0.1429 b) A student has just been given a 7-question multiple-choice...
. In a history class, Colin and Diana both write a multiple choice quiz. There are...
. In a history class, Colin and Diana both write a multiple choice quiz. There are 10 questions. Each question has five possible answers. What is the probability that Passing is considered 70% a) Colin will pass the test if he guesses an answer to each question. b) Diana will pass the test if she studies so that she has a 75% chance of answering each question correctly.