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 $\mathrm{B})$

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$, if $5$ appears on the first

 $\mathrm{A}$ die is thrown. If $\mathrm{E}$ is the event $'$ the number appearing is a multiple of $3'$ and $F$ be the event $'$ the number appearing is even $^{\prime}$ then find whether $E$ and $F$ are independent ?

Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is

Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$,  $ P ( B )=0.7$,  $P ( A \cap B )=0.6$