Question

Ms. Kandru gave a 4 question multiple choice quiz. Each question had 4 choices to select from. If the student completely guessed on every problem, what is the probability that they make a score of exactly a 50% (i.e. exactly 2 questions correct)?

a) 1/16
b) 3/16
c) 3/8
d) 1/2

Answer 1

The probability of a student scoring exactly 50% on the quiz can be calculated using the binomial probability formula.

Step-by-step explanation:

To find the probability that a student scores exactly 50% on the quiz, we need to consider the number of ways they can answer 2 questions correctly out of 4. Since there are 4 choices for each question, the student has a 1/4 chance of guessing each question correctly. Therefore, the probability of getting 2 questions correct is given by the binomial probability formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on each trial, and C(n, k) is the number of combinations of n items taken k at a time. In this case, n = 4, k = 2, and p = 1/4.

Using the formula, we have P(X = 2) = C(4, 2) * (1/4)^2 * (3/4)^2 = 6 * 1/16 * 9/16 = 54/256 = 27/128. Therefore, the probability that the student makes a score of exactly 50% is 27/128.