Question

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 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). _____________

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

(please explain the steps used to solve these)

Answer #1

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...

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 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 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 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 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 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 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 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 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.

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