Question

If two numbers p and q are chosen randomly from the set {1, 2, 3, 4}, one by one, with replacement, then the probability of getting p² ≥ 4q is

Options

• \[\frac{1}{4}\]

• \[\frac{7}{16}\]

• \[\frac{1}{2}\]

• \[\frac{9}{16}\]

Answer 1

\[\frac{7}{16}\]

Explanation:

Given set is {1, 2, 3, 4} and condition is p² ≥ 4q

∴ The following cases are possible

∴ Case 1: p = 2, q = 1
Case 2: p = 3, q = 1, 2
Case 3: p = 4, q = 1, 2, 3, 4

∴ Favourable cases = 7
Total cases = 4² = 16

∴ Required probability = \[\frac{7}{16}\]