GATE CSE
First time here? Checkout the FAQ!
x
0 votes
48 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)
asked in Probability by Active (1.8k points)   | 48 views

1 Answer

+1 vote
Best answer

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

 

 

answered by Boss (5.7k points)  
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) }
Top Users Jan 2017
  1. Debashish Deka

    9614 Points

  2. sudsho

    5554 Points

  3. Habibkhan

    4878 Points

  4. Bikram

    4774 Points

  5. Vijay Thakur

    4498 Points

  6. Arjun

    4408 Points

  7. saurabh rai

    4236 Points

  8. Sushant Gokhale

    4112 Points

  9. Kapil

    3830 Points

  10. santhoshdevulapally

    3808 Points

Monthly Topper: Rs. 500 gift card

19,371 questions
24,203 answers
53,828 comments
20,370 users