Given two mutually exclusive events $A$ and $B$ such that $P(A) = 0.45$ and $P(B) = 0.35,$ then $P (A$ or $B ) =$

One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent ?

$\mathrm{E}:$  ' the card drawn is black ' 

$\mathrm{F}:$  ' the card drawn is a king '

If $A$ and $B$ are two events such that $P\,(A \cup B) = P\,(A \cap B),$ then the true relation is

Events $E$ and $F$ are such that $P ( $ not  $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.

A bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be either red or blue.

The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are