Question 1151986: A multiple choice examination has 25 questions, each with 5 possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess.
a)Write the random variable representing the number of correct answers(+show that is correctly defined)
b) Which is the expected number of correct answers? (+calculations_
c)Which is the probability to have at least 2 correct answers?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! X=0,1,2,...,25 for a binomial distribution with n=25 and p=0.2
E(X)=25*0.2=5
probability of at least 2 correct answers is 1- p(0) and p(1)
the probability of 0 is 0.8^25=0.0038
prob of 1 is 25*0.2*0.8^24=0.0236
That sum is 0.0274, so probability of at least 2 is 1-0.0274 or 0.9726.
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