Question

An instructor gives his class a set of 15 problems with the information that the next quiz will consist of a random selection of 7 of them. if a student has figured out how to do 8 of the problems, what is the probability the he or she will answer correctly

(a) all 7 problems?

Answer 1

The probability that the student will answer all 7 problems correctly is calculated by dividing the number of favorable outcomes (C(8,7)) by the number of all possible outcomes (C(15,7)), giving a result of 8/6435.

Step-by-step explanation:

To find the probability that a student will answer all 7 questions correctly on a quiz with a random selection of 7 out of 15 problems, we can use the principles of combinatorics. Given that a student knows how to do 8 of the problems, the number of favorable outcomes (answering all 7 correctly) is the number of ways to choose 7 problems out of the 8 they know, which is calculated using combinations: C(8,7).

The total number of possible outcomes (any 7 questions from the 15) is C(15,7).

The probability is then given by:

P(correct answers) = C(8,7) / C(15,7)

Calculating C(8,7) is straightforward since there are 8 ways of choosing 7 problems from 8:

• C(8,7) = 8

To calculate C(15,7), use:

C(15,7) = 15! / (7! * (15-7)!) = 6435

Thus, the probability is:

P(correct answers) = 8 / 6435