Question

If two numbers p and q are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability that p² ≥ 4q is equal to ______.

Options

• `1/4`

• `3/16`

• `1/2`

• `7/16`

Answer 1

If two numbers p and q are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability that p² ≥ 4q is equal to `bbunderline(7/16)`.

Explanation:

Total number of outcomes

S = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)}

n(S) = 16

Number of favourable outcomes E = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (4,4)}

n(E) = 7

Required probability = `(n(E))/(n(S)) = 7/16`