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 $P\left(A \cap B^{\prime}\right)$
$\begin{array}{l} P\left(A \cap B^{\prime}\right)=P(A)-P(A \cap B) \\ =0.35-0 \end{array}$
$=0.35$
(b) We need to find $P\left(A^{\prime} \cap B^{\prime}\right)$
$\begin{array}{l} P\left(A^{\prime} \cap B^{\prime}\right)=P(A \cup B)^{\prime} \\ =1-P(A \cup B) \\ =1-0.8 \\ =0.2 \end{array}$