Answer:
a. The probability of getting exactly 6 of the question right is approximately 0.164
b. The probability of getting at most 6 of the questions right is approximately 0.93
Step-by-step explanation:
The given parameters are;
The number of multiple choice questions = 9 multiple choice questions
The number of options in each question = 3 options
The number of outcomes to the answers of the question = 2, Right or Wrong
Therefore, the probability of having a question right, p = 1/2
The probability of having a question wrong, q = 1 - p = 1 - 1/2 = 1/2
By binomial probability theorem, we have;
The probability of getting exactly 6 of the question right, P(6), is given as follows;
P(6) = ₉C₆·p⁶·(q)⁹⁻⁶ = 84 × (1/2)⁶ × (1/2)³ = 0.1640625
The probability of getting exactly 6 of the question right, P(6) = 0.1640625 ≈ 0.164
b. The probability of P(at most 6 of the questions right) = P(X ≤ 6)
P(at most 6 of the questions right) = P(X ≤ 6) = 1 - P(X ≥ 7)
∴ P(X ≤ 6) = 1 - (₉C₇·p⁷·q⁹⁻⁷) = 1 -(36·(1/2)⁷·(1/2)² = 0.9299875
The probability of P(at most 6 of the questions right) = P(X ≤ 6) = 0.9299875 ≈ 0.93.
