Probability Tes...

In throwing of a die, let $$A$$ be the event 'an odd humber turns up', $$B$$ be the event 'a number divisible by $$3$$ turns up' and $$C$$ be the event 'a number $$\leq 4$$ turns up', Then find the probability that exactly two of $$A, B$$ and $$C$$ occur.

For an event E, P(E) + P(E') =

If $$n(A)=18$$, $$n(B)=12$$, and $$A\cap B=\emptyset$$, then $$n(A\cup B)=$$

In a group of $$15$$ people $$7$$ read French $$8$$ read English while $$3$$ of them read none of them. How many read French and English both?

If A is any event in a sample space then P(A') is____

A couple has two children,
(i) Find the probability that both children are males, if it is known that at least one of the children is male.
(ii) Find the probability that both children are females, if ti is known that the elder child is a female.

Three letters, to each of which corresponds an envelope, are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes, is

The chance of throwing a total of $$3$$ or $$5$$ or $$11$$ with two dice is.

Given that the events $$A$$ and $$B$$ are such that $$P\left( A \right) = \displaystyle\frac { 1 }{ 2 } ,  P\left( A\cup B \right) = \displaystyle\frac { 3 }{ 5 } $$ and $$P\left( B \right) =p$$. Find $$p$$ if they are (i) mutually exclusive (ii) independent.

If $$A$$ and $$B$$ are any two events such that $$P\left( A \right) +P\left( B \right) -P\left( A  and  B \right) =P\left( A \right) $$, then