Fill in the blank in the following table:
P(A) P(B) P(A∩B) P(AυB)
(i) 1/3 1/5 1/15 ...
(ii) 0.35 ... 0.25 0.6
(iii) 0.5 0.35 ... 0.7

Solution:

Using P(A U B) formula, P (A υ B) = P (A) + P (B) - P (A ∩ B).

(i) Here, P (A) = 1/3, P (B) = 1/5, P (A ∩ B) = 1/15

We know that; P (A υ B) = P (A) + P (B) - P (A ∩ B)

Therefore,

P ( A υ B) = 1/3 + 1/5 - 1/15

= (5 + 3 - 1)/15

= 7/15

(ii) Here, P (A) = 0.35, P (A ∩ B) = 0.25, P (A υ B) = 0.6

We know that; P (A υ B) = P (A) + P (B) - P (A ∩ B)

Therefore,

P (B) = P (A υ B) - P (A) + P (A ∩ B)

= 0.6 - 0.35 + 0.25

= 0.85 - 0.35

= 0.5

(iii) Here, P(A) = 0.5, P(B) = 0.35, P(A υ B) = 0.7

We know that; P (A υ B) = P (A) + P (B) - P (A ∩ B)

Therefore,

P (A υ B) = P (A) + P (B) - P (A ∩ B)

P (A ∩ B) = P (A) + P (B) - P (A υ B)

= 0.5 + 0.35 - 0.7

= 0.85 - 0.7

= 0.15

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 13

Summary:

(i) P(A υ B) = 7/15 (ii) P(B) = 0.5 (iii) P(A ∩ B) = 0.15