If A and B are mutually exclusive events and if p(B)=(1/3),p(A∪ B)=(13/21), then P(A) is equal to

Question

If A and B are mutually exclusive events and if p(B)=(1/3),p(A∪ B)=(13/21), then P(A) is equal to (A)  (1/7)  (B)  (4/7)  (C)  (2/7)  (D)  (5/7)

Tardigrade Admin · Accepted Answer

We have p(B)=(1/3),p(A∪ B)=(13/21) For mutually exclusive events A and B, we get p(A∪ B)=p(A)+p(B) ⇒ p(A)=p(A∪ B)-p(B) =(13/21)-(1/3) =(13-7/21)=(6/21)=(2/7) ∴ p(A)=(2/7)

Q. If $A$ and $B$ are mutually exclusive events and if $p (B) = \frac{1}{3}, p (A \cup B) = \frac{13}{21},$ then $P (A)$ is equal to

$\frac{1}{7}$

$\frac{4}{7}$

$\frac{2}{7}$

$\frac{5}{7}$

$\frac{6}{7}$

We have $p (B) = \frac{1}{3}, p (A \cup B) = \frac{13}{21}$
For mutually exclusive events A and B, we get $p (A \cup B) = p (A) + p (B)$
$\Rightarrow$ $p (A) = p (A \cup B) - p (B)$
$= \frac{13}{21} - \frac{1}{3}$
$= \frac{13 - 7}{21} = \frac{6}{21} = \frac{2}{7}$
$∴$ $p (A) = \frac{2}{7}$

Q. If A and B are mutually exclusive events and if p(B)=31​,p(A∪B)=2113​, then P(A) is equal to

71​

74​

72​

75​

76​

We have p(B)=31​,p(A∪B)=2113​ For mutually exclusive events A and B, we get p(A∪B)=p(A)+p(B) ⇒ p(A)=p(A∪B)−p(B) =2113​−31​ =2113−7​=216​=72​ ∴ p(A)=72​