Shortcut:
Probability of an event (E) is denoted by P(E) and is defined as
P(E) =
n(E)
/
n(S)
=
No. of desired events
/
total number of events (ie no. of sample space)
In all the above cases, S = {1,2,3,4,5,6}
n(S) = 6
(i) E(an even no.) = {2,4,6}, n(E) = 3
∴ P(E) =
n(E)
/
n(S)
=
3
/
6
=
1
/
2
(ii) E(an odd no.) = {1,3,5}, n(E) = 3
∴ P(E) =
n(E)
/
n(S)
=
3
/
6
=
1
/
2
(iii) E(a no. divisible by 2) = {2,4,6}, n(E) = 3
∴ P(E) =
n(E)
/
n(S)
=
3
/
6
=
1
/
2
(iv) E(a no. divisible by 3) = {3,6}, n(E) = 2
∴ P(E) =
n(E)
/
n(S)
=
2
/
6
=
1
/
3
(v) E(a no. less than 4) = {1,2,3}, n(E) = 3
∴ P(E) =
n(E)
/
n(S)
=
3
/
6
=
1
/
2
(vi) E(a no. less than or equal to 4) = {1, 2, 3, 4}, n(E) = 4
∴ P(E) =
n(E)
/
n(S)
=
4
/
6
=
2
/
3
(vii) E(a no. greater than 6) = {}, i.e., there is no number greater than 6 in the sample space.
∴ P(E) =
n(E)
/
n(S)
=
0
/
6
= 0
Probability of an impossible event = 0
(viii) E(a no. less than or equal to 6) = {1,2,3,4,5, 6}, n(E) = 6
∴ P(E) =
n(E)
/
n(S)
=
6
/
6
= 1
Probability of a certain event = 1
Note: 0 ≤ P(E) ≤ 1
