If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find (a) P (A ∪ B) (b) P (A ∩ B)

Home » If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find (a) P (A ∪ B) (b) P (A ∩ B)

If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find
(a) P (A ∪ B)
(b) P (A ∩ B)

CBSE | Class 11 | Maths | NCERT Exemplar | Probability

If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find
(a) P (A ∪ B)
(b) P (A ∩ B)

Solution:

Given: $P(A)=0.35$ and $P(B)=0.45$
$\because$ The events $A$ and $B$ are mutually exclusive then $P(A \cap B)=0$
(a) We need to find $P(A \cup B)$
It is known that,
$\begin{array}{l} P(A \cup B)=P(A)+P(B)-P(A \cap B) \\ \Rightarrow P(A \cup B)=0.35+0.45-0 \text { [given }] \\ \Rightarrow P(A \cup B)=0.80 \end{array}$
(b) We need to find $P(A \cap B)$
It is given that $A$ and $B$ are mutually exclusive events.
$\therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=0$