Page 91 - Probability Demystified

80 CHAPTER 5 Odds and Expectation

1
When the probability of an event occurring is , then the odds are 1 : 1.
2
In the realm of gambling, we say the odds are ‘‘even’’ and the chance of the
event is ‘‘fifty–fifty.’’ The game is said to be fair. Odds can be other numbers,
such as 2 : 5, 7 : 4, etc.

PRACTICE

1. When two dice are rolled, find the odds in favor of getting a sum
of 12.
2. When a single card is drawn from a deck of 52 cards, find the odds
against getting a diamond.
3. When three coins are tossed, find the odds in favor of getting two tails
and a head in any order.
4. When a single die is rolled, find the odds in favor of getting an even
number.
5. When two dice are rolled, find the odds against getting a sum of 7.

ANSWERS

1. There is only one way to get a sum of 12, and that is (6, 6). There are
36 outcomes in the sample space. Hence, P(sum of 12) ¼ 1 : The
36
odds in favor are
1 1
36 ¼ 36 ¼ 1 35 ¼ 1 36 1 ¼ 1
1 35 36 36 36 1 35 35
1
36 36
The odds are 1 : 35.
13 1
^
2. There are 13 diamonds in 52 cards; hence, Pð ) ¼ ¼ :
1 3 52 4
^
Pð Þ¼ 1 ¼ : The odds against getting a diamond
4 4
3 3
1
3
4 ¼ 4 ¼ ¼ 3 4 1 ¼ 3
3 1 4 4 4 1 1 1
1
4 4
The odds are 3 : 1.