Answer:
0.9844
Step-by-step explanation:
This is a binomial probability problem.
Probability of getting a correct answer: p = 1/4
Probability of getting an incorrect answer: 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
