Question

Question 17 A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine (i) P(not A), (ii) P (not B) and (iii) P(A or B).

Class X1 - Maths -Probability Page 405

Answer 1

here, given that
P( A ) = 0.42
P( B ) = 0.48
P( A and B ) = 0.16 or, P( A ∩ B ) = 0.16

(I) P ( not A ) = P( A' ) = 1 - P( A )
⇒ P( not A ) = 1 - P( A )
P( not A ) = 1 - 0.42 = 0.58

(ii) P( not B) = P(B') = 1 - P( B )
⇒P( not B ) = 1 - P( B )
P( not B ) = 1 - 0.48 = 0.52

(Iii) P( A or B ) = P( A ∪ B ) = P( A ) + P( B ) - P( A ∩ B )
P( A or B ) = 0.42 + 0.48 - 0.16
P( A or B ) = 0.9 - 0.16 = 0.74