Cynthia is taking a test she is completely not prepared for, so she guesses on a
ID: 3043757 • Letter: C
Question
Cynthia is taking a test she is completely not prepared for, so she guesses on all 20 questions which each have 4 possible answers. Brian is not prepared for the test either and claims he guessed on all the questions too. What is the probability that Brian would have 10 or more answers that match Cynthia’s answers if he guessed on all the questions. Cynthia is taking a test she is completely not prepared for, so she guesses on all 20 questions which each have 4 possible answers. Brian is not prepared for the test either and claims he guessed on all the questions too. What is the probability that Brian would have 10 or more answers that match Cynthia’s answers if he guessed on all the questions.Explanation / Answer
Answer:
Cynthia is taking a test she is completely not prepared for, so she guesses on all 20 questions which each have 4 possible answers. Brian is not prepared for the test either and claims he guessed on all the questions too. What is the probability that Brian would have 10 or more answers that match Cynthia’s answers if he guessed on all the questions.
n=20, p=1/4=0.25
Binomial distribution used
P( x 10) = 0.0139
( excel function used: =1-BINOM.DIST(9,20,0.25,TRUE) )
probability that Brian would have 10 or more answers = 0.0139
probability that both match = 0.0139*0.0139
= 0.000193
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