Page 93 - Probability Demystified

82 CHAPTER 5 Odds and Expectation

EXAMPLE: If the odds that an event will occur are 5 : 7, find the probability
that the event will occur.

SOLUTION:

A
5
5
In this case, A ¼ 5 and B ¼ 7; hence, PðE Þ¼ AþB ¼ 5 þ 7 ¼ 12 : Hence, the
probability the event will occur is 5 :
12
EXAMPLE: If the odds in favor of an event are 2 : 9, find the probability that
the event will not occur.

SOLUTION:
In this case, A ¼ 2 and B ¼ 9; hence, the probability that the event will not
occur is
B 9 9
PðEÞ¼ ¼ ¼ :
B þ A 9 þ 2 11

PRACTICE

1. Find the probability that an event E will occur if the odds are 5:2 in
favor of E.
2. Find the probability that an event E will not occur if the odds against
the event E are 4 : 1.
3. Find the probability that an event E will occur if the odds in favor of
the event are 2 : 3.
4. When two dice are rolled, the odds in favor of getting a sum of 8 are
5 : 31; find the probability of getting a sum of 8.
5. When a single card is drawn from a deck of 52 cards, the odds against
getting a face card are 10 : 3, find the probability of selecting a face
card.

ANSWERS
5 5
1. Let A ¼ 5 and B ¼ 2; then PðE Þ¼ ¼ :
5 þ 2 7
4 4
2. Let B ¼ 4 and A ¼ 1; then PðEÞ¼ ¼ :
4 þ 1 5
2 2
3. Let A ¼ 2 and B ¼ 3; then PðE Þ¼ ¼ :
2 þ 3 5