Question

David didn’t study for his introduction to logic exam consisting of 15 true-false questions. He did blind guessing on each question. a. If he needs to score 10 or more correct to pass, what is the probability that he will fail the exam? b. Find the probability that he answers 6 to 11 (inclusive) questions correctly.

Answer 1

a) 0.1509

b) 0.8314

Explanation:

Since there are only two options for each question, the probability that he guesses right is p = 0.50, and the probability that he guesses wrong is q = 0.50

There is a total of 15 questions in the test so we can use the formula for a binomial distribution with parameters n = 15, p = 0.5, q = 0.5

a) If he needs to score 10 or more correct to pass, what is the probability that he will fail the exam?

To find this probability we will need to find the probability:

P ( X < 10) or

(1 - P (x ≥10))

Remember that the formula for a binomial distribution is:

`P(x) = \left[\begin{array}{ccc}n\\x\end{array}\right] p^(x) q^(n-x)`

We can solve this by using the parameters given before and make x = 10, 11, 12, 13, 14, 15 and use the formula:

P(he fails the exam) = 1 - P (x≥10)

= 1 - (P(x=10) + P(x=11) + P(x=12) + P(x=13) + P(x=14) + P(x=15))

= 0.1509

b) Find the probability that he answers 6 to 11 inclusive)

We're going to use the same formula but we will do:

P (x = 6) + P (x = 7) + P (x = 8) + P (x = 9) + P (x = 10) + P (x = 11)

=0.1527 + .1964 + .1964 + 0.1527 + 0.0916 + 0.0416

= 0.8314

Therefore the probability that he answers 6 to 11 inclusive is 0.8314