Question

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?

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

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...

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