th 21 Online Homework> Assessment Experiments and Binomial Distributions Muliple

Question

th 21 Online Homework> Assessment Experiments and Binomial Distributions Muliple-choice questions each have 3 possible answers, one of which is correct. Assume that you guess the answers to 4 such questions Use the multiplication rule to find the probability that the first three guesses are wrong and the fourth is correct. That is, find P(WWWC), where C denotes a correct answer and W denotes a wrong answer (round answer to 4 decimal places) What is the probability of getting exactly one correct answer when 4 guesses are made? (round answer to 4 decimal places) Ptexactly one correct answer) Points possible: 1 This is attempt 1 of 3 FS F7 F8 F9 F1O

Explanation / Answer

P(correct answer) = 1/3
P(wrong answer) = 1-1/3 = 2/3

By using multiplication rule
i) P(WWWC) = 2/3 * 2/3 * 2/3 * 1/3 = 8/81 = 0.0988

ii) When Binomial distribution is used
n = 4
p = 1/3
q = 1-p = 1-1/3 = 2/3

P(r) = nCr*p^r*q^(n-r)
Required probability = P(r=1) = 4C1*(2/3)^3*(1/3)^1
= 4*8/27*1/3
= 32/81

= 0.3951

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