Page 78 - Probability Demystified

CHAPTER 4 The Multiplication Rules 67

EXAMPLE: When two dice were rolled, it is known that the sum was an even
number. In this case, find the probability that the sum was 8.

SOLUTION:

When rolling two dice, there are 18 outcomes in which the sum is an even
number. There are 5 ways to get a sum of 8; hence, P(sum of 8|sum is
4
even) is 8 or .
18 9

EXAMPLE: In a large housing plan, 35% of the homes have a deck and
a two-car garage, and 80% of the houses have a two-car garage. Find the
probability that a house has a deck given that it has a garage.

SOLUTION:
Pðdeck and two-car garageÞ¼ 0:35 and Pðtwo-car garageÞ¼ 0:80; hence;
(deck and two-car garage)
P(deckjtwo-car garage) ¼
P(two-car garage)
0:35
¼
0:80
7
¼ or 0:4375
16

PRACTICE

1. When two dice are rolled, find the probability that one die is a 6 given
that the sum of the spots is 8.
2. Two coins are tossed. Find the probability of getting two tails if it is
known that one of the coins is a tail.
3. A card is selected from a deck. Find the probability that it is an ace
given that it is a black card.
4. The probability that a family visits the Sand Crab Water Park and
the Rainbow Gardens Amusement Park is 0.20. The probability
that a family visits the Rainbow Gardens Amusement Park is 0.80.
Find the probability that a family visits the Sand Crab Water Park
if it is known that they have already visited Rainbow Gardens
Amusement Park.
5. Three dice are rolled. Find the probability of getting three twos if it is
known that the sum of the spots of the three dice was six.