Probability Tes...

A box contain $$N$$  coins,  $$m$$  of which are fair and rest are biased. The probability of getting a head when a fair coin is tossed is $$\dfrac{1}{2}$$, while it is $$\dfrac{2}3{}$$. when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. The probability that the coin drawn is fair is

It is given that event A & B are such that $$\displaystyle P(A)=\frac{1}{4},P\left(\frac{A}{B}\right)=\frac{1}{2},P\left(\frac{B}{A}\right)=\frac{2}{3},$$ then $$\displaystyle P(B)=$$

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 $$50$$.

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.

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.

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 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.

There are two bags, one of which contains three black and four white balls while the other contains four black and three white balls. A die is cast: if the face 1 or 3 turns up, a ball is taken from the first bag; and if any other face turns up, a ball is chosen from the second bag. Find the probability of choosing a black ball.

A letter is known to have come eithe from London or Clifton; on the post only the consecutive letters ON are legible; what is the chance that it came from London?