Expand Your Knowledge: Odds Against Betting odds are usually stated against the event happening (against winning). The
Question:
Expand Your Knowledge: Odds Against Betting odds are usually stated against the event happening
(against winning).
The odds against event W are the ratio P not W P W P W P W c
5
( )
( )
( )
( )
.
In horse racing, the betting odds are based on the probability that the horse does not win.
(a) Show that if we are given the odds against an event W as a:b, the probability of not W is P W a
a b c 5 1
( ) .
Hint: Solve the equation a
b P W P W c
c 5
2
( )
1 ( )
for P(Wc ).
(b) In a recent Kentucky Derby, the betting odds for the favorite horse, Point Given, were 9 to 5. Use these odds to compute the probability that Point Given would lose the race. What is the probability that Point Given would win the race?
(c) In the same race, the betting odds for the horse Monarchos were 6 to 1. Use these odds to estimate the probability that Monarchos would lose the race.
What is the probability that Monarchos would win the race?
(d) Invisible Ink was a long shot, with betting odds of 30 to 1. Use these odds to estimate the probability that Invisible Ink would lose the race. What is the probability the horse would win the race? For further information on the Kentucky Derby, visit the web site of the Kentucky Derby.
AppendixLO1
Step by Step Answer:
Understandable Statistics Concepts And Methods
ISBN: 9780357719176
13th Edition
Authors: Charles Henry Brase, Corrinne Pellillo Brase