Question

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

$\frac{7}{16}$

Given set is $\{1,2,3,4\}$ and condition is $p^2\le 4q$

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 $=4^2=16$

Required probability $=\frac{7}{16}$