For events $A$ and $B$, it is given that $P(A)=\dfrac{1}{4}$, $P(A\cup B)=\dfrac{5}{8}$

Question

For events $A$ and $B$, it is given that $P(A)=\dfrac{1}{4}$, $P(A\cup B)=\dfrac{5}{8}$ and $P(A\cap B')=\dfrac{1}{8}$. Find $P(B)$.[1] Determine, with a reason, whether the events $A$ and $B$ are independent.[2] For a third event $C$, it is given that $P(C)=\dfrac{2}{5}$, $P(A\cap B\cap C)=\dfrac{1}{20}$, and $C$ is independent of $A$. Find $P(A'\cap C)$.[1] Find the range of possible values of $P(A'\cap B'\cap C')$.[3]

Accepted Answer

(i) $\dfrac{1}{2}$ (ii) Independent (iii) $\dfrac{3}{10}$ (iv) $\dfrac{3}{40}\le P(A'\cap B'\cap C')\le\dfrac{3}{8}$

Solution:

Typed Solution