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

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

If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45,
find (a) P (A′) (b) P (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) P (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 $P\left(A^{\prime}\right)$
It is known that,
$P(A)+P\left(A^{\prime}\right)=1$
$\Rightarrow 0.35+P\left(A^{\prime}\right)=1[\text { given }]$
$\Rightarrow P\left(A^{\prime}\right)=1-0.35$
$\Rightarrow P\left(A^{\prime}\right)=0.65$
(b) We need to find $P\left(B^{\prime}\right)$
It is known that,
$P(B)+P\left(B^{\prime}\right)=1$
$\Rightarrow 0.45+P\left(B^{\prime}\right)=1$
$\Rightarrow P\left(B^{\prime}\right)=1-0.45$
$\Rightarrow P\left(B^{\prime}\right)=0.55$