You are taking a 6 question multiple choice quiz, each question has 4 possible answers, what is the probability of getting exactly 5 questions right?
The answer is 0.00439 , but how do i get to that answer? I have a review sheet for my test but it doesn't explain the steps. Can anyone help?
The answer is 0.00439 , but how do i get to that answer? I have a review sheet for my test but it doesn't explain the steps. Can anyone help?
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Use the binomial distribution for n=6 trials, success probability p=1/4 on each trial, and exactly k=5 successes:
(6 choose 5)(1/4)^5 [1 - (1/4)]^(6-5) = [6!/(5!(6-5)!)] (1/4)^5 (3/4)
= [6!/(5!1!)] (3/(4^6))
= [6*5*4*3*2*1 / (5*4*3*2*1*1)](3/4096)
= 18/4096
= 9/2048 or about 0.00439
Lord bless you today!
(6 choose 5)(1/4)^5 [1 - (1/4)]^(6-5) = [6!/(5!(6-5)!)] (1/4)^5 (3/4)
= [6!/(5!1!)] (3/(4^6))
= [6*5*4*3*2*1 / (5*4*3*2*1*1)](3/4096)
= 18/4096
= 9/2048 or about 0.00439
Lord bless you today!
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Use a Binomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. If the probability of success on an individual trial is P, then the binomial probability is:
b(x; n, P) = nCx * P^x * (1 - P)^(n - x)
b(5; 6,.25) = 6C5 *.25^5 *(1 - .25)^(6-5)
= .00439453125 or .00439 (rounded off)
b(x; n, P) = nCx * P^x * (1 - P)^(n - x)
b(5; 6,.25) = 6C5 *.25^5 *(1 - .25)^(6-5)
= .00439453125 or .00439 (rounded off)