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)

Solution:

It is given that P (A) = 0.42, P (B) = 0.48 and P (A and B) = 0.16

(i) We know that

P (not A) = 1 - P (A)

= 1 – 0.42

= 0.58

(ii) We know that

P (not B) = 1 - P (B)

= 1 – 0.48

= 0.52

(iii) Using the addition theorem of probability,

P (A or B) = P (A) + P (B) - P (A and B)

= 0.42 + 0.48 – 0.16

= 0.74

---

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 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).

Summary:

If A and B are events such that P (A) = 0.42, P (B) = 0.48 and P (A and B) = 0.16 then

(i) P(not A) = 0.58 (ii) P(not B) = 0.52 (iii) P(A or B) = 0.74