Question

3) Suppose a student is taking a multiple-choice question exam in which each answer has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on the following strategy: She will place four balls marked A, B, C, and D in a box. She randomly selects one ball for each question and replaces the ball in the box after marking the letter of the ball as the answer. If there are 25 multiple-choice questions on the exam, what is the probability that she will get:a) 10 questions correct?
b) at least 5 questions correct?
c) 8 questions correct?
d) fewer than 8 questions correct?

Answer 1

n=25 ; P=Y4 = 0.25 P(X=x) =(22. p* q hx a) Plox= 10) = (25 ) (6.25) 0 (1-0.25 5-10 = 0.0416 6) P(x 25) = 1-P(+24) 21- [ PCX=02 +P(X=) +P(X=e) HCX23) HP (X= 4) a 1-(0.01374) 10.7863) c) P(X= 8) = (25)(025)(-0.25).** 25-8 d) - 10.1241 P(X28)= P(x=0) + P(x-1) +----+ P(x-7) = 10.7265