Practicing Success
If $P(A)=\frac{6}{11},P(B)=\frac{5}{11}$ and $P(A ∪ B)=\frac{7}{11},$ then A. $P(A ∩ B)=\frac{4}{11}$ B. $P(A | B)=\frac{4}{5}$ C. $P(B | A)=\frac{2}{5}$ D. A and B are independent evennts E. P(neither A nor B) $=\frac{4}{11}$ |
A and E only A, B and E only B and D only A, C and E only |
A, B and E only |
The correct answer is Option (2) → A, B and E only $P(A)=\frac{6}{11},P(B)=\frac{5}{11}$, $P(A ∪ B)=\frac{7}{11}$ so $P(A∩B)=P(A)+P(B)-P(A ∪ B)=\frac{4}{11}$ $P(A).P(B)≠P(A∩B)$ ⇒ A, B not independent $P(A|B)=P(A)=\frac{6}{11},P(B|A)=P(B)=\frac{5}{11}$ P(neither A nor B) = $P(\overline{A ∪ B})=\frac{4}{11}$ A, B and E only are true |