Page 77 - Probability Demystified

66 CHAPTER 4 The Multiplication Rules

SOLUTION:

P(A and B) is the probability of getting a 4 and an even number at the same
time. Notice that there is only one way to get a 4 and an even number—the
1
outcome 4. Hence P(A and B) ¼ . Also P(B) is the probability of getting an
6
3
1
even number which is ¼ . Now
6 2
PðA and BÞ
PðAjBÞ¼
PðBÞ
1
6
¼
1
2
1 1
¼
6 2
1 2 1
¼
6 3 1
1
¼
3
Notice that the answer is the same as the answer obtained when classical
probability was used.
EXAMPLE: Two dice are rolled. Find the probability of getting a sum of 3 if
it is known that the sum of the spots on the dice was less than 6.

SOLUTION:

P(A and B) means the probability of getting a sum of 3 and a sum less than 6.
Hence P(A and B) ¼ 2 : PðBÞ means getting a sum less than 6 and is 10 .
36 36
Hence,
2
PðA and BÞ 36
PðAjBÞ¼ ¼
PðBÞ 10
36
2 10
¼
36 36
1
2 36
¼
36 10 5
1
¼
5