Because they are so easy to correct, multiple-choice questions are commonly used

Question

Because they are so easy to correct, multiple-choice questions are commonly used for class tests. Consider a 10 multiple-choice question test. Each question has 5 possible answers (a. b, c, d, e), one of which is correct. Assume that random guesses are made for each of the 10 questions. In particular you should: find the probability distribution P(x), where x is the number of correct responses when someone makes random guesses for the multiple-choice questions, and verify that the table satisfies the requirements for a probability distribution.

Explanation / Answer

(a) n = 10, p = 1/5 = 0.2, q = 1 - p = 0.8, and x varies from 0 to 10

P(x) = C(n, x) p^x q^(n - x)

P(0) = C(10, 0) 0.2^0 0.8^(10 - 0) = 0.1074

P(1) = C(10, 1) 0.2^1 0.8^(10 - 1) = 0.2684

P(2) = C(10, 2) 0.2^2 0.8^(10 - 2) = 0.3020

Similarly, P(3) = 0.2013, P(4) = 0.0881, P(5) = 0.0264, P(6) = 0.0055, P(7) = 0.0008, P(8) = 0.0001, P(9) = 0, P(10) = 0

(b) In the above table, all P(x) values lie between 0 and 1 inclusive, and the sum of all the values is 1. Thus the table satisfies the requirements of a probability distribution.

Number of correct responses (x) P(x) 0 0.1074 1 0.2684 2 0.3020 3 0.2013 4 0.0881 5 0.0264 6 0.0055 7 0.0008 8 0.0001 9 0.0000 10 0.0000

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.