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(1) In a throw of a coin, find the probability of getting a tail.

Soln. Here, S = { H, T } ( i.e. n = 2 ) and A = { H } ( i.e. m = 1 ).

$\therefore$ P ( A ) = $\frac{m}{n}$ = $\frac{1}{2}$ .

(2) Two unbiased coins are tossed. What is the probability of getting exactly 1 tail ?

Soln. Here, S = { HH, HT, TH, TT } ( i.e. n = 4 )

Let, A = Event of getting at most one head.

A = {HT, TH} ( i.e. m = 2 ).

$\therefore$ P(A) = $\frac{m}{n}$ = $\frac{3}{6}$ = $\frac{1}{2}$

(3) An unbiased die is tossed. Find the probability of getting a prime number.

Soln. Here, S = {1, 2, 3, 4, 5, 6} ( i.e. n = 6 )

Let, A be the event of getting a prime number.

$\therefore$ A = { 2, 3, 5 }. ( i.e. m = 3 ).

$\therefore$ P ( A ) = $\frac{m}{n}$ = $\frac{3}{6}$ = $\frac{1}{2}$ .

In a simultaneous throw of a pair of dice
Sum of numbers	Event	No. of repetitions
2	{ (1, 1) }	1
3	{ (1, 2), (2, 1) }	2
4	{ (1, 3), (2, 2), (3, 4) }	3
5	{ (1, 4), (2, 3), (3, 2), (4, 1) }	4
6	{ (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) }	5
7	{ (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) }	6
8	{ (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) }	5
9	{ (3, 6), (4, 5), (5, 4), (6, 3) }	4
10	{ (4, 6), (5, 5), (6, 4) }	3
11	{ (5, 6), (6, 5) }	2
12	{ (6, 6) }	1