Probability Tes...

An experiment can result in only 3 mutually exclusive events A, B and C. If  $$ \displaystyle P\left ( A \right )=2P\left ( B \right )=3P\left ( C \right ), $$ then $$ \displaystyle P\left ( A \right ) $$ equals

A die is thrown :
$$P$$ is the event of getting an odd number.
$$Q$$ is the event of getting an even number.
$$R$$ is the event of getting a prime number.

$$A$$ and $$ B$$ are events such that $$\displaystyle p(A \cup B) =3/4,P(A\cap B)=\frac{1}{4},P(\bar{A})=\frac{2}{3}$$, then $$\displaystyle P((\bar{A}\cap B)$$ equals

Form two digit numbers using the digit $$0,1,2,3,4,5$$ without repeating the digits.
$$P$$ is the event that the number so formed is even.
$$Q$$ is the event that the number so formed is divisible by $$3$$.
$$R$$ is the event that the number so formed is greater than $$50$$.

If $$P(A)\, =\, \displaystyle \frac{3}{4} ,\, P(B')\, =\, \frac{1}{3}\, and\, P(A \cap B)\, =\, \frac{1}{2}\,$$ then find $$P(A \cup B)$$.

There are $$3$$ men and $$2$$ women. a 'Gramswachhatta Abhiyan' committee of two is to be formed :
$$P$$ is event that the committee should contain at least one woman.
$$Q$$ is event that the committee should contain one man and one women.
$$R$$ is the event there should not be a women in the committee.

A card is drawn at random from well shuffled pack of $$52$$ cards. Find the probability that the card drawn is a spade:

A and B are two events on a sample space S such that $$P(A) = 0.8 , P(B) = 0.6$$ and $$P(A \cup B) = 0.9$$ find $$(A \cap B)$$.

There are $$3$$ red, $$3$$ white and $$3$$ green balls in a bag. One ball is drawn at random from a bag:
$$P$$ is the event that ball is red.
$$Q$$ is the event that ball is not green.
$$R$$ is the event that ball is red or white.

If two coins are tossed then find the probability of the event of getting one head .