What is the probability that the number 3 has appeared at least once

Event A indicates the combination in which 3 has appeared at least once that is A = {(3, 1), (3, 2), (3, 3)(3, 4)(3, 5)(3, 6)(1, 3)(2, 3)(4, 3)(5, 3)(6, 3)}

Event B indicates the combination of the numbers which sum up to 7 that is
B = {(1, 6)(2, 5)(3, 4)(4, 3)(5, 2)(6, 1)}

probability of event A

P(A) = \$\frac(1)(36)\$

probability of event B

P(B) = \$\frac(6)(36)\$

according to the question the intersection that is happening of two events

A ∩ B = 2

probability of intersection of two evevnts

P(A ∩ B) = \$\frac(2)(36)\$

conditional probability \$P(A/B) = (P(A∩B)) / (P(B))\$

Simplification

\$\frac(2)(36) /\frac(6)(36)\$

After simplification we get

\$\frac(1)(3)\$

Answer

C