A student takes a true false test but did not study and randomly guess each questions there are 20 questions on the test.

Question

A student takes a true false test but did not study and randomly guess each questions there are 20 questions on the test. Find the probability that the student passes test with a grade of 70% or higher?

Answer 1

There are 20 true-false questions on the test. In order to get a 70% on the test, a student needs to get 14 correct questions.

The probability of getting a question right is 0.50 or 50%.

P(Passing the Test) = C(20, 14)*[(0.5)¹⁴ × (0.5)⁶] + C(20, 15)*[(0.5)¹⁵ × (0.5)⁵] + C(20, 16)*[(0.5)¹⁶ × (0.5)⁴] + C(20, 17)*[(0.5)¹⁷ × (0.5)³] + C(20, 18)*[(0.5)¹⁸ × (0.5)²] + C(20, 19)*[(0.5)¹⁹ × (0.5)¹] + C(20, 20)*[(0.5)²⁰ × (0.5)⁰]

= 0.05766

The probability of a student passing a test with a 70% or higher is 0.05766.