The odds against Rainbow winning the race are 17:5. Brian bets $120 on Rainbow to win and Rainbow does win the race.
How much money does Brian win? What was the probability that Rainbow was going to win the race?
Lay/Aniya/Brianna -- please use the same name for your posts.
pr(win)=17/22
How much does he win?
win=120/(17/22)=120*22/17
(minus fees and track takings)
To determine how much money Brian wins and the probability of Rainbow winning the race, we need to understand what the odds of 17:5 mean.
In odds notation, the odds against an event happening are expressed as a ratio of the number of unfavorable outcomes to the number of favorable outcomes. In this case, for Rainbow to win the race, there are 5 favorable outcomes (Rainbow winning) and 17 unfavorable outcomes (Rainbow not winning).
To calculate the amount of money Brian wins, we need to calculate the profit earned from the bet. The profit is equal to the amount won minus the amount staked.
First, let's calculate the amount won:
Amount won = Amount staked × (Total return / Amount staked) = $120 × (1 + Odds)
Considering the odds against Rainbow winning are 17:5, the total return can be calculated as follows:
Total return = Amount staked + Profit
Since we are interested in the profit, let's rearrange the formula:
Profit = Total return - Amount staked
Now, let's calculate the total return:
Total return = Amount staked × (17 + 5) / 5
Plugging in the values, we have:
Total return = $120 × (17 + 5) / 5 = $120 × 22 / 5
Therefore, the total return is $528.
Now, we can determine the profit:
Profit = Total return - Amount staked = $528 - $120 = $408
Therefore, Brian wins $408 in the race.
To calculate the probability that Rainbow was going to win the race, we need to convert the odds into probabilities. The probability of an event is the favorable outcomes divided by the total number of outcomes.
In this case, the probability that Rainbow was going to win the race is:
Probability = Favorable outcomes / Total outcomes
Since the odds are in a ratio of 17:5, the total number of outcomes is the sum of the favorable and unfavorable outcomes:
Total outcomes = 17 + 5 = 22
Therefore, the probability of Rainbow winning the race is:
Probability = 5 / 22 ≈ 0.227
So, the probability that Rainbow was going to win the race is approximately 0.227 or 22.7%.