If $$A, B$$ and $$C$$ are three independent events such that $$P(A)=P(B)=P(C)=P$$, then $$P$$ (at least two of $$A, B$$ and $$C$$ occur) is equal to

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

A car manufacturing factory has two plants $$X$$ and $$Y$$. Plant $$X$$ manufactures $$70 \%$$ of cars and plant $$Y$$ manufactures $$30 \%$$ of cars. $$80 \%$$ of cars at plant $$X$$ and $$90 %$$ of cars at plant $$Y$$ are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant $$X$$ is :

If $$P(A)=0.59, P(B)=0.30$$ and $$P(A \cap B)=0.21$$ then $$P\left(A^{\prime} \cap B^{\prime}\right)$$ is equal to