If A and B are two independent events with P(A) = 5 and P(B) = 9 , then P ( A ) equals to

P ( A ) = 1 - P(A B) = 1 - [P(A) + P(B) - P(A B)] = 1 - = 1 - = 1 - 45 = 45 = 9

Probability — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.69,Page.281

Question

If A and B are two independent events with $P(A) = \frac{3}{5}$ and $P(B) = \frac{4}{9}$, then $P\left( {{A^\prime } \cap {B^\prime }} \right)$ equals to

(a) $\frac{4}{{15}}$
(b) $\frac{8}{{45}}$
(c) $\frac{1}{3}$
(d) $\frac{2}{9}$ ✓ Correct

Step-by-step Solution

$P\left( {{A^\prime } \cap {B^\prime }} \right) = 1 - P(A \cup B)$

$= 1 - [P(A) + P(B) - P(A \cap B)]$

$= 1 - \left[ {\frac{3}{5} + \frac{4}{9} - \frac{3}{5} \times \frac{4}{9}} \right]$

$= 1 - \left[ {\frac{{27 + 20 - 12}}{{45}}} \right] = 1 - \frac{{35}}{{45}} = \frac{{10}}{{45}} = \frac{2}{9}$

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