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Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find (i) $P(A \cap B)$ (ii) $P(A \cup B)$ (iii) $P(A \mid B)$ (iv) $P(B \mid A)$
Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find (i) $P(A \cap B)$
(ii) $P(A \cup B)$
(iii) $P(A \mid B)$
(iv) $P(B \mid A)$
CBSE | Maths | NCERT | Probability
Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find (i) $P(A \cap B)$
(ii) $P(A \cup B)$
(iii) $P(A \mid B)$
(iv) $P(B \mid A)$

Given $P ( A )=0.3$ and $P ( B )=0.4$

(i) $P(A \cap B)$

When A and B are independent. Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

$\Rightarrow P(A\cap B)=P(A)\cdot P(B)$

$\Rightarrow P(A\cap B)=0.3\times 0.4\Rightarrow P(A\cap B)=0.12$

$(ii)$

As we know, $$P(A \cup B)=P(A)+P(B)-P(A \cap B)$$

$$\Rightarrow P(A \cup B)=0.3+0.4-0.12$$

$$\Rightarrow P(A \cup B)=0.58$$

(iii) $P ( A \mid B )$

As we know $$P(A \mid B)=\frac{P(A \cap B)}{P(B)}$$

$$P(A\mid B)=\frac{0.12}{0.4}\Rightarrow P(A\mid B)=0.3$$

$(iv)$

As we know $$P(B \mid A)=\frac{P(A \cap B)}{P(A)}$$

$$\Rightarrow P(B\mid A)=\frac{0.12}{0.3}\Rightarrow P(B\mid A)=0.4$$

i

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