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. $\frac{9}{16}$
• E. $\frac{7}{16}$

Answer 1

Answer: (E)

56.Given set is $\{1,2,3,4\}$ and condition is $p^{2} \geq 4 q$
Therefore, the following cases are possible
(i) $p=2, q=1$
(ii) $p=3, q=1,2$
(iii) $p=4, q=1,2,3,4$
$\therefore $ Favourable cases $=7$
And total number of cases $=4^{2}=16$
$\therefore $ Required probability $=\frac{7}{16}$