Question

A test contains 10 multiple choice questions, each with four possible answers. If a student was to simply guess what the answers are, then we can model the final number of questions this student gets correct as a binomial distribution Bn,p) with n= S and p= If the pass mark is 5 out of 10, what is the probability that this student will pass the test? It is (to 5 decimal places) 3 What is the probability the student gets at most 2 out of 10? It is (to 5 decimal places)

Answer 1

To calculate the probability of passing the test, we can use the binomial distribution formula. For at least 70% score, we calculate the probability of getting 5 or more correct answers out of 10 questions. For at most 2 correct answers, we calculate the probability of getting 0, 1, or 2 correct answers out of 10 questions.

Step-by-step explanation:

The probability of passing the test with a score of at least 70% can be found by calculating the probability of getting 5, 6, 7, 8, 9, or 10 correct answers out of the 10 multiple choice questions. The probability of guessing a single question correctly is 1/4, so the probability of getting k questions correct out of n questions is given by the binomial distribution formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination formula.

To calculate the probability of passing with at most 2 correct answers, we need to calculate the probability of getting 0, 1, or 2 correct answers out of the 10 questions. We can use the same binomial distribution formula to calculate each individual probability and then sum them up.