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**tfhawk** Problem: A person is take a multiple choice exam that has 6 questions. Each question has 5 possible choices. The person decides to randomly guess at each problem. Let x be the number of questions the person will answer correctly. Construct the probability distribution, and answer the following:

Find P(x<=2)

Find P(2<=x<=4)

Find the expected value of x

Find the variance of x

What i know: I know the probability of answering a question correctly is (1/5) and the probability for answering a question incorrectly is (4/5). I also know that each question is independent of the others. To find the probabilities for my distribution I used [(1/5)^n]*[(4/5)^m] where n is the number of correctly answered questions and m is the number of incorrectly answered questions. My probability distribution is:

X P(x)

0 .26

1 .07

2 .02

3 .004

4 0

5 0

6 0

This doesn't seem like it could be correct. Any help would be appreciated.