Question

Question 12 Check whether the following probabilities P(A) and P(B) are consistently defined

(i) P(A) = 0.5, P(B) = 0.7, P(A∩B) = 0.6

(ii) P(A) = 0.5, P(B) = 0.4, P(A∪B) = 0.8

Class X1 - Maths -Probability Page 405

Answer 1

concept : For consistent P(A ∩ B ) must be less than or equal to P( A ) and P( B )

( i ) P( A ∩ B ) < P( B )
but P( A ∩ B ) > P( A ) this is against of concept for consistency .
hence, given data is not consistent .

(ii) we know,
P( A U B ) = P( A ) + P( B ) - P( A ∩ B )
0.8 = 0.5 + 0.4 - P( A ∩ B )
P( A ∩ B ) = 0.1
here, it's clear that
P( A ∩ B ) < P( A )
P( A ∩ B ) < P( B )
hence, P( A ) and P( B ) are BC consistent

Answer 2

I HOPE IT WILL HELP YOU.

THANK YOU.