A teacher gave a 3-question multiple choice quiz. Each question had 4 choices to select from. If the a student completely guessed on every problem, what is the probability that they will have 2 or less correct answers?

0.9844

Step-by-step explanation:

This is a binomial probability problem.

Probability of getting a correct p = 1/4

Probability of getting an incorrect q = 3/4

Number of questions; n = 3

Thus;

probability of 2 or less correct answers is; P(x ≤ 2) = P(X = 2) + P(X = 1) + P(X = 0)

From binomial probability the formula is;

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

P(X = 2) = C(3, 2) × (¼)² × (¾)¹

P(X = 2) = 3 × 0.0625 × 0.75

P(X = 2) = 0.1406

P(X = 1) = C(3, 1) × (¼)¹ × (¾)²

P(X = 1) = 3 × 0.25 × 0.5625

P(X = 1) = 0.4219

P(X = 0) = C(3, 0) × (¼)^(0) × (¾)³

P(X = 0) = 0.4219

P(x ≤ 2) = 0.1406 + 0.4219 + 0.4219

P(x ≤ 2) = 0.9844

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^