Question

Research has shown that studying improves a student's chances to $80\%$ of selecting the correct answer to a multiple choice question. A multiple choice test has 15 questions. Each question has 4 choices and exactly one is correct.
Suppose that a student does not study for the test but randomly guesses the answers. The probability that the student will answer 7 or 8 questions correctly when he attempts all, is

• A. ${}^{15}{C}_7\cdot {\left(\frac{1}{5}\right)}^7\cdot {\left(\frac{4}{5}\right)}^7$
• B. ${}^{15}{C}_7\cdot {\left(\frac{1}{3}\right)}^7\cdot {\left(\frac{2}{3}\right)}^7$
• C. ${}^{15}{C}_7\cdot {\left(\frac{1}{4}\right)}^7\cdot {\left(\frac{3}{4}\right)}^7$
• D. can't be determined

Answer 1

Answer: (C)

Correct answer is (c) ${}^{15}{C}_7\cdot {\left(\frac{1}{4}\right)}^7\cdot {\left(\frac{3}{4}\right)}^7$