Question

(4 points) An instructor gives his class a set of 11 problems with the information that the next quiz will consist of a random selection of 5 of them. If a student has figured out how to do 10 of the problems, what is the probability the he or she will answer correctly?

Answer 1

Answer:

6/11 = 0.545

Step-by-step explanation:

We use combination theory. The total number of ways in which 5 questions can be selected out of 11 is ¹¹C₅ since it is a random selection and order doesn't matter. The total number of ways in which the student can answer 5 questions with him knowing 10 out of 11 is ¹⁰C₅. Since it doesn't matter the order of questions he can answer out of the 11, we do not do ¹¹C₁₀ which is the number of ways he can choose correctly out of the 11 questions. The probability that he will get the answer right = event space/ sample space = ¹⁰C₅/¹¹C₅ = $\frac{10!}{5!5!}$÷$\frac{11!}{5!6!}$ = 6/11 = 0.545