Question

Fill in the blanks in following table:

| P(A)| P(B)| P(A∩B)| P(A∪B)
---|---|---|---|---
(i)| $\frac{1}{3}$| $\frac{1}{5}$| $\frac{1}{15}$| …
(ii)| 0.35| ….| 0.25| 0.6
(iii)| 0.5| 0.35| ….| 0.7

Answer 1

(i) Here,$P(A)=\frac{1}{3},P(B)=\frac{1}{5},P(A∩B)=\frac{1}{15}$

We know that $P(A∪B)=P(A)+P(B)-P(A∩B)$

$∴P(AUB)=\frac{1}{3}+\frac{1}{5}-\frac{1}{15}=5+3-\frac{1}{15}=\frac{7}{15}$

(ii) Here, $P(A) = 0.35, P(A ∩ B) = 0.25, P(A U B) = 0.6$
We know that $P(A U B) = P(A) + P(B) \- P(A ∩ B)$

$∴0.6 = 0.35 + P(B) \- 0.25$
$⇒ P(B) = 0.6 \- 0.35 + 0.25$
$⇒ P(B) = 0.5$

(iii) Here, $P(A) = 0.5, P(B) = 0.35, P(A U B) = 0.7$
We know that $P(A U B) = P(A) + P(B) -P(A ∩ B)$

$∴0.7 = 0.5 + 0.35- P(A ∩ B)$
$⇒ P(A \cap B) = 0.5 + 0.35 \- 0.7$
$⇒ P(A ∩ B) = 0.15$