A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three
Decimal places.
A) 0.172
B) 0.377
C) 0.205
D) 0.828

Question

Quizplus · Accepted Answer

The probability of getting any one question correct by guessing is 1/2. Since there are 10 questions, the number of ways to get exactly 6 questions correct is given by the binomial distribution with n = 10 and p = 1/2:
P(X = 6) = (10 choose 6) * (1/2)^6 * (1/2)^4 = 0.205
Similarly, we can find the probabilities of getting exactly 7, 8, 9, or 10 questions correct and add them together, since passing the test requires getting at least 6 questions correct:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
P(X ≥ 6) = 0.205 + 0.246 + 0.205 + 0.102 + 0.028 = 0.786
Rounding to three decimal places, we get 0.786, which matches choice B.

A Test Consists of 10 True/false Questions