Question

If A and B are any two events having 1 ( ) 2 P A B   and 2 ( ) 3 P A  then the probability of A B  is

Answer 1

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ANSWER

Going by options:

(a) Minimum value of P(A∩B) is the higher of P(A) and P(B) i.e. 32 and maximum value is 1. So, (a) is true.

(b) Maximum intersection of P(A∩Bˉ) is the minimum of P(A) and P(Bˉ) i.e. minimum of  21 and 31 = 31. So, (b) is true.

(c) P(A)+P(B)=21+32=67. Hence, P(A∩B)≥67−1=61. 

Again, maximum intersection of P(A∩B) is the minimum of P(A) and P(B) i.e. minimum of  21 and 32 = 21. So, (c) is true.

(d) Maximum intersection of P(B∩Aˉ) is the minimum of P(B) and P(Aˉ) i.e. minimum of  32 and 2