Question

Two dice are thrown simultaneously, The probability of obtaining a total score of seven is $\frac{k}{36}$. Find the value of $k$.

Answer 1

There are 6 numbers (1,2,3,4,5,6) written on the six faces of each die.
Thus there are six possible ways as to the number of points on the first die;and to each of these ways, there correspond 6 possible numbers of points on the second die
Hence the total no. of ways $n=6\times 6=36$
We now find out how many ways are favourable to the total of 7 points.
This may happen only in the following ways:(1,6), (6,1), (2,5), (5,2), (3,4), and (4,3), that is, in 6 ways,
where first member of each ordered pair denotes the number on the first die and second member denotes the number of second die
$\therefore m=6,$
Hence required probability $=\frac{m}{n}=\frac{6}{36}=\frac{1}{6}.$