Probability Tes...

A coin is tossed and a die is thrown simultaneously :
$$P$$ is the event of getting head and a odd number.
$$Q$$ is the event of getting either $$H$$ or $$T$$ and an even number.
$$R$$ is the event of getting a number on die greater than $$7$$ and a tail.

Two dice are thrown :
$$P$$ is the event that the sum of the scores on the uppermost faces is a multiple of $$6$$.
$$Q$$ is the event that the sum of the scores on the uppermost faces is at least $$10$$.
$$R$$ is the event that same scores on both dice.

Two die are thrown find the probability of getting the sum of the numbers on their upper faces divisible by 9.

In a certain city two newspapers $$A$$ and $$B$$ are published. It is known that $$25$$% of the city population reads $$A$$ and $$20\%$$ of the population reads $$B$$. $$8\%$$ of the population reads both $$A$$ and $$B$$. It is known that $$30$$% of those who read $$A$$ but not $$ B $$ look into advertisements and $$40$$% of those who read $$B$$ but not $$A$$ look advertisements while $$50$$% of those who read both $$A$$ and $$B$$ look into advertisements . What is the percentage of the population who reads an advertisement?

The probability of an event A occurring is $$0.5$$ and of B occuring s $$0.3$$. If A and B are mutually exclusive events, then the probability of neither  A nor B occurring is

A coin is tossed twice. Events E and F are defined as follows :E=heads on first toss, F= heads on second toss.Find the probability of $$\displaystyle E\cup F.$$

In a class of $$100$$ students, $$60$$ students drink tea, $$50$$ students drink coffee and $$30$$ students drink both. A student from class is selected at random, find the probability that student takes at least one of the two drinks (i.e. tea or coffee or both).

If A and B are arbitrary events, then

There are n different object 1, 2, 3, ... n distributed at random in n boxes $$\displaystyle A_{1},A_{2},A_{3},\cdots A_{N}.$$ Find the probability that two objects are placed in the boxes corresponding to their number.