H S Hall and S R Knight Solutions for Chapter: Probability, Exercise 1: EXAMPLES. XXXII. a.

There are three events $A$, $B$ and $C$ one of which must, and only one can happen; the odds are $8$ to $3$ against $A$ and $5$ to $2$ against $B$, find the odds against $C$.

Compare the chances of throwing $4$ with one dice, $8$ with two dice and $12$ with three dice.

In shuffling a pack of cards, four are accidentally dropped, Find the chance that the missing cards should be one from each suit.

There are three works, one containing of $3$ volumes, one of $4$ volumes and the other of $1$ volume. They are placed on a shelf at random, prove that the chance that the volumes of the same works are all together is $\frac{3}{140}$.

$A$ and $B$ throw with two dice, if $A$ throws $9$, find $B\text{'}s$ chance of throwing a higher number.

The letters forming the word 'Clifton" are placed at random in a row, what is the chance that the two vowels come together?

In a hand at whist what is the chance that the $4$ kings are held by a specified player?

There are $4$ rupees and $3$ ten paisa coins placed at random in a line, show that the chance that the extreme coins being both ten paisa is $\frac{1}{7}$. Generalize this result in the case of $m$ rupees and $n$ ten paisa.