odds that the horse will lose = 5 : 3
so the prob it will lose is 5/8
and the prob it will win is 3/8
odds in favour of some event happening
= prob(the event will happen) : prob(the event will not happen)
how do you start this?
so the prob it will lose is 5/8
and the prob it will win is 3/8
odds in favour of some event happening
= prob(the event will happen) : prob(the event will not happen)
1. Convert the given odds of 5 to 3 into "odds in favor" format.
- Odds against represent the ratio of the probability that an event will not occur to the probability that it will occur.
- Odds in favor represent the ratio of the probability that an event will occur to the probability that it will not occur.
To convert the odds against to odds in favor, subtract the denominator from the numerator:
- Odds in favor = odds against - 1
In this case, the odds against are 5 to 3, so the odds in favor would be:
- Odds in favor = 5 - 3 = 2
2. Calculate the probability of winning using the odds in favor.
- Probability of winning = 1 / (odds in favor + 1)
Using the odds in favor of 2, the probability of the horse winning the race can be calculated as:
- Probability of winning = 1 / (2 + 1) = 1/3
Therefore, the probability of the horse winning the race is 1/3 or approximately 0.33.
In this case, the odds listed as 5 to 3 mean that for every 5 ways the horse will not win, there are 3 ways it will win. To find the probability of winning, you can use the following formula:
Probability of winning = 1 / (odds against + 1)
Now, let's calculate the probability of the horse winning the race:
Odds against winning = 5 (number of ways the horse will not win)
Odds in favor of winning = 3 (number of ways the horse will win)
Probability of winning = 1 / (5 + 1) = 1/6 ≈ 0.1667
Therefore, the probability of the horse winning the race is approximately 0.1667 or 16.67%.