99 views
If P and Q are two random events, then the following is TRUE:

A] Independence of P and Q implies that probability (P ∩ Q) = 0
B] Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)
C] If P and Q are mutually exclusive, then they must be independent
D] Probability (P ∩ Q) ≤ Probability (P)

+1 vote

here i check option---> i let P = probability,  P and Q is replaced by A and B.

A) it  is saying independent means P(A ^ B) =  P(A)* P(B)  so option A is false

B) P(AÜ B) =  P(A) + P(B) - P(A ^ B)

hence P(AÜ B) >= P(A) + P(B)  its false option B is false

C) if A and B is mutually exclusive means P(A ^ B) =  0 then its independent ........its false  there is no relation independent and mutually exclusive

D)  P(A^ B) <= P(A)

its true

hence option D is correct

selected by

First three options are false for sure but still not satisfied with last one. Can you please elaborate more, @Hradesh patel ?

u think this way   A ^ B  <=  A     ////  in this line" < "denotes subset

n(A  ^  B ) <=  n(A)

P(A ^ B) <=  P(A)

i hope this help u
Yeah, this helped.

To be more precise, I think this should be like

Probability (P ∩ Q) ≤ min{ Probability (P), Probability (Q) }