If A and B are two events such that P(B) = 5 ,P(A/B) = 2 and P(A B) = 5 , then P(A) equals to

Here, P(B) = 5 ,P(A/B) = 2 and P(A B) = 5 P(A/B) = P(B) 2 = 3/5 P(A B) = 5 2 = 10 and P(A B) = P(A) + P(B) - P(A B) 5 = P(A) + 5 - 10 P(A) = 5 - 5 + 10 = 10 = 2

Probability — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.64,Page.280

Question

If A and B are two events such that $P(B) = \frac{3}{5},P(A/B) = \frac{1}{2}$ and $P(A \cup B) = \frac{4}{5}$, then $P(A)$ equals to

(a) $\frac{3}{{10}}$
(b) $\frac{1}{5}$
(c) $\frac{1}{2}$ ✓ Correct
(d) $\frac{3}{5}$

Step-by-step Solution

Here, $P(B) = \frac{3}{5},P(A/B) = \frac{1}{2}$ and $P(A \cup B) = \frac{4}{5}$

$P(A/B) = \frac{{P(A \cap B)}}{{P(B)}}$

$\Rightarrow$ $\frac{1}{2} = \frac{{P(A \cap B)}}{{3/5}}$
$\Rightarrow$ $P(A \cap B) = \frac{3}{5} \times \frac{1}{2} = \frac{3}{{10}}$

and $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow$ $\frac{4}{5} = P(A) + \frac{3}{5} - \frac{3}{{10}}$

$\therefore$ $P(A) = \frac{4}{5} - \frac{3}{5} + \frac{3}{{10}} = \frac{{8 - 6 + 3}}{{10}} = \frac{1}{2}$

← All Probability solutions Practice tests →

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.