Question

# Three events $$A$$, B and $$C$$ have probabilities $$\dfrac{2}{5}, \dfrac{1}{3}$$ and $$\dfrac{1}{2}$$ respectively. Given that $$P(A \cap B)=\dfrac{1}{5}$$ and $$P(B \cap C)=\dfrac{1}{4},$$ find the value of $$P(C \mid B)$$ and $$P\left(A^{\prime} \cap C^{\prime}\right)$$

Solution

## Here, $$P(A)=\dfrac{2}{5}, P(B)=\dfrac{1}{3}, P(C)=\dfrac{1}{2} \cdot P(A \cap C)=\dfrac{1}{5}$$ and $$P(B \cap C)=\dfrac{1}{4}$$$$\therefore P(C / B)=\dfrac{P(B \cap C)}{P(B)}=\dfrac{1 / 4}{1 / 3}=\dfrac{3}{4}$$And $$P\left(A^{\prime} \cap C\right)=1-P(A \cup C)=1-[P(A)+P(C)-P(A \cap C)]$$$$=1-\left[\dfrac{2}{5}+\dfrac{1}{2}-\dfrac{1}{5}\right]=1-\left[\dfrac{4+5-2}{10}\right]=1-\dfrac{7}{10}=\dfrac{3}{10}$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More