Answer to Question #163018 in Statistics and Probability for Sunny

Question

There are 16 questions each with 5 multiple choices. What is the probability of answering exactly 7 questions correctly?

Answer 1

If there are 5 multiple answers, the probability of right answer is 0.2. So the probability to answer correctly on 7 particular questions is 0.2⁷*0.8^16-7 = 0.2⁷*0.8⁹. And we need to multiply this by C₁₆⁷ - binomial coefficient, which means how many variants exist to choose 7 of 16 without order. So the probability is C₁₆⁷ * 0.2⁷*0.8⁹ = 0.0196..