GATE CSE
First time here? Checkout the FAQ!
x
0 votes
107 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 Loyal (3.3k points)   | 107 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 (6.4k 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 Jun 2017
  1. Bikram

    3912 Points

  2. Arnab Bhadra

    1526 Points

  3. Hemant Parihar

    1502 Points

  4. Niraj Singh 2

    1501 Points

  5. Debashish Deka

    1480 Points

  6. junaid ahmad

    1432 Points

  7. pawan kumarln

    1286 Points

  8. Rupendra Choudhary

    1242 Points

  9. rahul sharma 5

    1240 Points

  10. Arjun

    1232 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 Jun 26 - Jul 02
  1. pawan kumarln

    418 Points

  2. akankshadewangan24

    334 Points

  3. Arjun

    272 Points

  4. Debashish Deka

    234 Points

  5. Abhisek Das

    230 Points


23,433 questions
30,149 answers
67,606 comments
28,485 users