The document contains solutions to 3 probability problems: 1) Finding the probability of rolling a die with a face that is a multiple of 3 or 5. The probability is 5/6. 2) Finding the probability that a randomly selected digit between 1-50 is a multiple of 10 or 11. The probability is 18/50. 3) Finding the probability that a randomly drawn card is a queen or king. The probability is 8/52.

2. Example-10:
A die is rolled once. Find the probability the face is multiple of 3 or
multiple of 5.
Solution:
S = {1, 2, 3, 4, 5, 6}
n (S) = 6
Let A = face is multiple of 3
A = {3, 6}
n (A) = 2
Let B = face is multiple of 5
B = {5}
n (B) = 1
thus the event A and B are mutually exclusive events.
Therefore
( ) ( )
( ) 6
2
Sn
An
AP ==
( ) ( )
( ) 6
1
Sn
Bn
BP ==
= BA
( ) ( ) ( ) 5.0
6
3
6
1
6
2
==+=+= BPAPBAP

3. Example-11:
A digit is selected at random from the first 50 natural numbers, find
the probability that the selected digit is multiple of 10 or multiple of
11 .
Solution:
S = {1, 2, 3, ……, 49, 50}
n (S) = 50
Let A = digit is multiple of 10
A = {10, 20, 30, 40, 50}
n (A) = 5
Let B = digit is multiple of 11
B = {11, 22, 33, 44}
n (B) = 4
Find thus the event A and B are mutually exclusive events.
Therefore
( ) ( )
( ) 50
5
Sn
An
AP ==
( ) ( )
( ) 50
4
Sn
Bn
BP ==
= BA
( ) ( ) ( ) 18.0
50
9
50
4
50
5
==+=+= BPAPBAP

4. Example-12:
A card is selected at random from a deck of playing cards. Find the
probability that the card is a queen or a king.
Solution:
n (S) = 52
Let A = the card is a queen
n (A) = 4
Let B = the card is a king
n (B) = 4
Find thus the event A and B are mutually exclusive events
therefore
( ) ( )
( ) 52
4
Sn
An
AP ==
( ) ( )
( ) 52
4
Sn
Bn
BP ==
= BA
( ) ( ) ( ) 1538.0
52
8
52
4
52
4
==+=+= BPAPBAP