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) $P (A | B)$
(iv) $P (B | A)$

Open in App

Solution

It is given that $P (A) = 0.3$ and $P (B) = 0.4$
(i) If $A$ and $B$ are independent events, then
$P (A \cap B) = P (A) \cdot P (B) = 0.3 \times 0.4 = 0.12$
(ii) It is known that, $P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$\Rightarrow P (A \cup B) = 0.3 + 0.4 - 0.12 = 0.58$
(iii) It is known that, $P (A | B) = \frac{P (A \cap B)}{P (B)}$
$\Rightarrow P (A | B) = \frac{0.12}{0.4} = 0.3$
(iv) It is known that, $P (B | A) = \frac{P (A \cap B)}{P (A)}$
$\Rightarrow P (B | A) = \frac{0.12}{0.3} = 0.4$

Suggest Corrections

Similar questions

Let A and B be independent events with P (A) = 0.3 and P (B) = 0.4. Find

(i) P (A ∩ B) (ii) P (A ∪ B)

(iii) P (A|B) (iv) P (B|A)

A

B

P (A) = 0.2, P (B) = 0.5

P (A | B)

P (B | A)

P (A \cap B)

P (A \cup B)

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4 Find
$P (\frac{A}{B})$ .

Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find
$P (A \cup B)$

Let A and B be independent events with P (A ) = 0.3 and P (B) = 0.4 . Find
$P (A \cap B)$

$P (A \cup B)$

$P (\frac{A}{B})$ .

$P (\frac{B}{A})$

Join BYJU'S Learning Program