Question

If two numbers $p$ and $q$ are chosen randomly from the set $\\{1, 2, 3, 4\\}$ with replacement, then the probability that $p^2 \ge 4q$ is equal to

• A. $\frac{1}{4}$
• B. $\frac{3}{16}$
• C. $\frac{1}{2}$
• D. $\frac{7}{16}$

Answer 1

Answer: (D)

$\frac{7}{16}$

Answer 2

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 $E = \\{(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (4,4)\\}$ $n(E) = 7$ $\therefore$ Required probability $= \frac{n\left(E\right)}{n\left(S\right) }$ $= \frac{7}{16}$