Clearly, the sample space is given by
S
=
{
1
,
2
,
3
,
4
,
5
,
.
.
,
19
,
20
}
and, n(S) = 20.
(i) Let
E
1
=
event of getting a prime number. Then,
E
1
=
{
2
,
3
,
5
,
7
,
11
,
13
,
17
,
19
}
and, therefore,
n
(
E
1
)
=
8
.
∴
P(getting a prime number)
=
P
(
E
1
)
=
n
(
E
1
)
n
(
S
)
=
8
20
=
2
5
.
(ii) Let
E
2
=
event of getting on odd number. Then,
E
2
=
{
1
,
3
,
5
,
7
,
9
,
11
,
13
,
15
,
17
,
19
}
and, therefore,
n
(
E
2
)
=
10
.
(iii) Let
E
3
=
event of getting a multiple of 5. Then,
E
3
=
{
5
,
10
,
15
,
20
}
and, therefore,
n
(
E
3
)
=
4
.
∴
P(getting a multiple of 5)
=
P
(
E
3
)
=
n
(
E
3
)
n
(
S
)
=
4
20
=
1
5
.
(iv) Let
E
4
=
event of getting a number which is not divisible by 3.
Then,
E
4
=
{
1
,
2
,
4
,
5
,
7
,
8
,
10
,
11
,
13
,
14
,
16
,
17
,
19
,
20
}
and so,
n
(
E
4
)
=
14
.
∴
P(getting a number which is not divisible by 3)
P
(
E
4
)
=
n
(
E
4
)
n
(
S
)
=
14
20
=
7
10
.
