Probability Tes...

A letter is known to have come either from $$LONDON$$ or $$CLIFTON$$; on the postmark only the two consecutive letters $$ON$$ are ellegible. The probability that it came from $$LONDON$$ is 

Two aeroplanes $$I$$ and $$II$$ bomb a target in succession. The probability of $$I$$ and $$II$$ scoring a hit correctly are $$0.3$$ and $$0.2$$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

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If $$E_{1}$$ and $$E_{2}$$ are two events such that $$\displaystyle P\left ( E_{1} \right )=\frac{1}{4}, P\left ( E_{2} \right )=\frac{1}{2}; P\left ( \frac{E_{1}}{E_{2}} \right )=\frac{1}{4},$$ then choose the correct options.

A black and a red dice are rolled.
(a) Find the conditional probability of obtaining a sum greater than $$9$$, given that the black die resulted in a $$5$$.
(b) Find the conditional probability of obtaining the sum $$8$$, given that the red die resulted in a number less than $$4$$. 

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl ?

One ticket is drawn from a bag containing 70 tickets numbered 1 to 70 Find the probability that it is a multiple of 5 or 7

Two coins are tossed once, where
(i) $$E$$ : tail appears on one coin,  $$F$$ : one coin shows head
(ii) $$E$$ : no tail appears,  $$F$$ : no head appears
Determine $$P\left( E|F \right) $$

If a vowel is selected at random from the English alphabet then what is the probability that it is U?

Let $$X$$ represent the difference between the number of heads and the number of tails obtained when a coin is tossed $$6$$ times. What are possible values of $$X$$ ?