P ( A )=(4/5), P ( B ')=(2/5) and P ( A ∩ B )=(1/2), then P ( A ∩ B ') equals.

Question

P ( A )=(4/5), P ( B ')=(2/5) and P ( A ∩ B )=(1/2), then P ( A ∩ B ') equals. (A) (2/7) (B) (1/5) (C) (3/10) (D) (1/10)

Tardigrade Admin · Accepted Answer

P ( B )=1 -P(B')= l -(2/5)=(3/5) ∵ P ( A ∪ B ) = P ( A )+ P ( B )- P ( A ∩ B ) =(4/5)+(3/5)-(1/2)=(9/10) ∴ P ( A ∩ B ') = P ( A ∪ B )- P ( B ) =(9/10)-(3/5)=(3/10)

Q. $P (A) = \frac{4}{5}, P (B^{^{'}}) = \frac{2}{5}$ and $P (A \cap B) = \frac{1}{2}$ , then $P (A \cap B^{^{'}})$ equals.

$\frac{2}{7}$

$\frac{1}{5}$

$\frac{3}{10}$

$\frac{1}{10}$

$\frac{2}{5}$

$P (B) = 1 - P (B^{^{'}}) = l - \frac{2}{5} = \frac{3}{5}$
$∵ P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$= \frac{4}{5} + \frac{3}{5} - \frac{1}{2} = \frac{9}{10}$
$∴ P (A \cap B^{^{'}}) = P (A \cup B) - P (B)$
$= \frac{9}{10} - \frac{3}{5} = \frac{3}{10}$

Q. P(A)=54​,P(B′)=52​ and P(A∩B)=21​, then P(A∩B′) equals.

72​

51​

103​

101​

52​

P(B)=1−P(B′)=l−52​=53​ ∵P(A∪B)=P(A)+P(B)−P(A∩B) =54​+53​−21​=109​ ∴P(A∩B′)=P(A∪B)−P(B) =109​−53​=103​