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

Question

If two numbers p and q are chosen randomly from the set 1, 2,3,4 with replacement, then the probability that p2 ge 4q is equal to (A) (1/4) (B) (3/16) (C) (1/2) (D) (9/16)

Tardigrade Admin · Accepted Answer

56.Given set is 1,2,3,4 and condition is p2 ≥ 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 ∴ Favourable cases =7 And total number of cases =42=16 ∴ Required probability =(7/16)

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

$\frac{1}{4}$

$\frac{3}{16}$

$\frac{1}{2}$

$\frac{9}{16}$

$\frac{7}{16}$

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) $p = 4, q = 1, 2, 3, 4$
$∴$ Favourable cases $= 7$
And total number of cases $= 4^{2} = 16$
$∴$ Required probability $= \frac{7}{16}$

Q. 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

41​

163​

21​

169​

167​

56.Given set is {1,2,3,4} and condition is p2≥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 ∴ Favourable cases =7 And total number of cases =42=16 ∴ Required probability =167​