Posted by **Collie** on Wednesday, October 3, 2012 at 8:33pm.

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 not be equal, but are equal. They should be equal, but may not be due to table error. 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 this Question

## Related Questions

- statistics - Richard has been given a 5-question multiple-choice quiz in his ...
- Statistics - Richard has been given a 5-question multiple-choice quiz in his ...
- Statistics - On a very short quiz, there is one multiple choice question with 5 ...
- stats - You took a 5-question multiple choice quiz with 4 choices for each ...
- Math - A multiple choice quiz contains five question. Each question has four ...
- Binomial Distribution - A biology quiz consists of twelve multiple-choice ...
- Statistic - There are two independent multiple-choice quizzes where quiz 1 has ...
- statistic and probability - There are two independent multiple-choice quizzes ...
- Statistics - You have a ten question multiple choice test in your next class and...
- Statistic - A quiz consists of 10 multiple-choice questions. Each question has 5...