Solution Found!
Odds of winning a race. Handicappers for greyhound races
Chapter 3, Problem 25E(choose chapter or problem)
Problem 25E
Odds of winning a race. Handicappers for greyhound races express their belief about the probabilities that each greyhound will win a race in terms of odds. If the probability of event E is P(E), then the odds in favor of E are P(E) to 1 - P(E). Thus, if a handicapper assesses a probability of .25 that Oxford Shoes will win its next race, the odds in favor of Oxford Shoes are 25/100 to 75/100, or 1 to 3. It follows that the odds against E are 1 - P(E) to P(E), or 3 to 1 against a win by Oxford Shoes. In general, if the odds in favor of event E are a to b, then P(E) = a/(a + b).
a. A second handicapper assesses the probability of a win by Oxford Shoes to be 1/3 . According to the second handicapper, what are the odds in favor of Oxford Shoes winning?
b. A third handicapper assesses the odds in favor of Oxford Shoes to be 1 to 1. According to the third handicapper, what is the probability of Oxford Shoes winning?
c. A fourth handicapper assesses the odds against Oxford Shoes winning to be 3 to 2. Find this handicapper’s assessment of the probability that Oxford Shoes will win.
Questions & Answers
QUESTION:
Problem 25E
Odds of winning a race. Handicappers for greyhound races express their belief about the probabilities that each greyhound will win a race in terms of odds. If the probability of event E is P(E), then the odds in favor of E are P(E) to 1 - P(E). Thus, if a handicapper assesses a probability of .25 that Oxford Shoes will win its next race, the odds in favor of Oxford Shoes are 25/100 to 75/100, or 1 to 3. It follows that the odds against E are 1 - P(E) to P(E), or 3 to 1 against a win by Oxford Shoes. In general, if the odds in favor of event E are a to b, then P(E) = a/(a + b).
a. A second handicapper assesses the probability of a win by Oxford Shoes to be 1/3 . According to the second handicapper, what are the odds in favor of Oxford Shoes winning?
b. A third handicapper assesses the odds in favor of Oxford Shoes to be 1 to 1. According to the third handicapper, what is the probability of Oxford Shoes winning?
c. A fourth handicapper assesses the odds against Oxford Shoes winning to be 3 to 2. Find this handicapper’s assessment of the probability that Oxford Shoes will win.
ANSWER:
Solution:
Step 1 of 4:
It is given that if the probability of an event E is P(E), then odds favour of E are P(E) to 1-P(E) and odds against E are 1-P(E) to P(E).
The handicappers have a belief in probabilities of winning a race i9n terms of odds.
The odds favouring the event E in general is given by
P(E)=
Using this we have to obtain the required values.