Page 72 - Probability Demystified

CHAPTER 4 The Multiplication Rules 61

PRACTICE

1. A card is drawn from a deck, then replaced, and a second card is
drawn. Find the probability that two kings are selected.
2. If 12% of adults are left-handed, find the probability that if three
adults are selected at random, all three will be left-handed.
3. If two people are selected at random, find the probability that both
were born in August.
4. A coin is tossed 4 times. Find the probability of getting 4 heads.
5. A die is rolled and a card is selected at random from a deck of 52
cards. Find the probability of getting an odd number on the die and a
club on the card.

ANSWERS

1. The probability that 2 kings are selected is
4 1 4 1 1
Pðking and kingÞ¼ PðkingÞ PðkingÞ¼ 13 13 ¼
52 52 169
2. The probability of selecting 3 adults who are left-handed is
(0.12)(0.12)(0.12) ¼ 0.001728.
3. Each person has approximately 1 chance in 12 of being born in
August; hence, the probability that both are born in August is
1 1 1
¼ :
12 12 144
1 1 1 1 1
4. The probability of getting 4 heads is ¼ .
2 2 2 2 16
3
1
5. The probability of getting an odd number on the die is ¼ , and the
6 2
1
probability of getting a club is 13 ¼ ; hence, the P(odd and
52
4
1
1
1
club) ¼ PðoddÞ PðclubÞ¼ ¼ .
2 4 8
Multiplication Rule II
When two sequential events are dependent, a slight variation of the
multiplication rule is used to find the probability of both events occurring.
For example, when a card is selected from an ordinary deck of 52 cards the