Set, Relation and FunctionHard
Question
Consider two sets A = {1,2,3} & B = {1,2,3,4,5}. A number is selected each from set A & set B. Let p denotes the probability that the selected number from set A is not more than the selected number from set-B & q denotes the probability that the number from set-B is not more than the number from set A, then -
Options
A.p = 2q
B.2p = 3q
C.p + q = 
D.p + q = 
Solution
Let Ai : Number i is selected from A.
Bj : Number j is selected from B.
⇒ p = P(n(A) ≤ n(B)) = 1 - P(n(A) > n(B))
= 1 - {P(A2).P(B1) + P(A3).P(B1 or B2)}
= 1 -
= P(n(B) ≤ n(A))
= P(A1).P(B1) + P(A2).P(B1 or B2)
+ P(A3)P(B1 or B2 or B3)
q =
Bj : Number j is selected from B.
⇒ p = P(n(A) ≤ n(B)) = 1 - P(n(A) > n(B))
= 1 - {P(A2).P(B1) + P(A3).P(B1 or B2)}
= 1 -
= P(n(B) ≤ n(A))= P(A1).P(B1) + P(A2).P(B1 or B2)
+ P(A3)P(B1 or B2 or B3)
q =
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