The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P (A ∩ B) = .07. Determine
(a) P (A ∪ B)
(b) P (A ∩ B)
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P (A ∩ B) = .07. Determine
(a) P (A ∪ B)
(b) P (A ∩ B)

NCERT Exemplar Solutions For Class 11 Maths Chapter 16 - Image 9

Solution:

It is given that \mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.07
From the Venn Diagram given

(a) P(A \cup B)
Using the General Addition Rule,
P(A \cup B)=P(A)+P(B)-P(A \cap B)
Substitute the values now,
\begin{array}{l} \Rightarrow P(A \cup B)=0.20+(0.07+0.10+0.15)-0.07 \\ \Rightarrow P(A \cup B)=0.20+0.25 \\ \Rightarrow P(A \cup B)=0.45 \end{array}
( b) \mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})
It is known that,
\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})
From the part (a) it can be written as
=0.20-0.07
=0.13