Let $A$ and $B$ be independent events such that $\mathrm{P}(\mathrm{A})=\mathrm{p}, \mathrm{P}(\mathrm{B})=2 \mathrm{p} .$ The largest value of $\mathrm{p}$, for which $\mathrm{P}$ (exactly one of $\mathrm{A}, \mathrm{B}$ occurs $)=\frac{5}{9}$, is :

Prove that if $E$ and $F$ are independent events, then so are the events $\mathrm{E}$ and $\mathrm{F}^{\prime}$.

If $\mathrm{A}$ and $\mathrm{B}$ are two events such that $\mathrm{P}(\mathrm{A})=\frac{1}{4}, \mathrm{P}(\mathrm{B})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{8}$ find $\mathrm{P}$ $($ not $\mathrm{A}$ and not $\mathrm{B})$

If $P(A) = 2/3$, $P(B) = 1/2$ and ${\rm{ }}P(A \cup B) = 5/6$ then events $A$ and $B$ are

In a city $20\%$ persons read English newspaper, $40\%$ read Hindi newspaper and $5\%$ read both newspapers. The percentage of non-reader either paper is

The probability that $A$ speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact