Richard has just been given a 6-question multiple-choice quiz in his history cla

Question

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 incorrectly? use the rule for mutually exclusive ivents and t (c) what is the probability that he will answer at least one of the questions correctly, Compute this probability two ways First, les shown in the binemial probability distribution table. Then use the fact that R21)-1-Ar·0). the fact that Pr 21)1 ence? Compare They should be equal, but may not be due to table error. O They should be equal, but differ substantially 0 They should not be equal, but are equal. They should be equal, but may differ sightly due to rounding error (d) What is the probability that Richard will answer at least haif the questions correctly?

Explanation / Answer

As there are 4 options for each question. He will randomly choosen any option and it will be the right option then .

Pr( Right ) = 1/4 and Pr( wrong) = 3/4

and total questions = 6

(A) Pr(Her will answer all question correctly) = 6C6 (0.25)6 = 0.0002

(B) Pr(He will answer all question incorrectly) = 6C6 (0.75)6 = 0.1780

(C) Pr(He will answer at least one question correctly) = 1 - Pr(will answer all question incorreect)

= 1 - 0.1780 = 0.8220

by binomial table Probability = 0.8220

Yes, both the answers are same

(D) Pr(at least 3 out of 6 questions are correct) = Pr(X =3) + Pr(X = 4) + Pr( X= 5) + Pr( X = 6)

=  6C3 (0.25)3 (0.75)3 + 6C4 (0.25)4 (0.75)2 + 6C5 (0.25)5 (0.75)1 +  6C6 (0.25)6

= 0.1318 + 0.0329 + 0.0044 + 0.0002

= 0.1694

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.