Given two mutually exclusive events $A$ and $B$ such that $P(A) = 0.45$ and $P(B) = 0.35,$ then $P (A$ or $B ) =$
$0.1$
$0.25$
$0.15$
$0.8$
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that First ball is black and second is red.
$A, B, C$ are any three events. If $P (S)$ denotes the probability of $S$ happening then $P\,(A \cap (B \cup C)) = $
The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$, then $P(A') + P(B') = $
In class $XI$ of a school $40\%$ of the students study Mathematics and $30 \%$ study Biology. $10 \%$ of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
If the odds against an event be $2 : 3$, then the probability of its occurrence is