The odds against Paul Phillips winning the 100 yard dash are 7:2. Determine the probability that:
• a) Paul wins.
• b) Paul does not win.
How do I set this up to find out the equation/answer?
When you say 7:2 odds against, what is really meant is that 7:2 are the odds on Paul winning. If you bet $2, you win $7 and get your $2 back also.
7:2 odds on paul means: There are 2 chances out of 9 (the sum of 7 and 2) that he will win and 7 chances out of 9 that he will not win
a) 2/9 = 22.2%
b) 7/9 = 77.8%
To determine the probability, you can use the formula:
Probability (P) = favorable outcomes / total outcomes
a) To find the probability of Paul winning the 100 yard dash, you need to determine the favorable outcomes and total outcomes.
In this case, the odds against Paul winning are 7:2. This means that for every 7 unfavorable outcomes, there are 2 favorable outcomes.
The total number of outcomes would be the sum of favorable and unfavorable outcomes. Therefore, the total number of outcomes is 7 + 2 = 9.
So, the probability of Paul winning is:
P(Paul wins) = favorable outcomes / total outcomes
P(Paul wins) = 2 / 9
b) To find the probability of Paul not winning, you need to determine the favorable outcomes for Paul not winning, which in this case would be 7, and the total number of outcomes, which is still 9.
So, the probability of Paul not winning is:
P(Paul does not win) = favorable outcomes / total outcomes
P(Paul does not win) = 7 / 9
To determine the probability that Paul Phillips wins the 100 yard dash, you need to set up the probability ratio using the given odds against him.
In this case, the odds against Paul winning are given as 7:2. This means that for every 7 successful outcomes (Paul doesn't win), there are 2 unsuccessful outcomes (Paul wins).
To set up the equation, you can write it as:
Probability of Paul winning = (Number of successful outcomes)/(Total number of outcomes)
Since the odds against Paul winning are 7:2, the total number of outcomes is the sum of the 7 and 2, which is 9.
a) Probability that Paul wins:
Since there are 2 successful outcomes (Paul wins), the probability that Paul wins the 100 yard dash can be calculated as:
Probability of Paul winning = 2/9 ≈ 0.222 or 22.2%
b) Probability that Paul does not win:
Since there are 7 unsuccessful outcomes (Paul doesn't win), the probability that Paul does not win the 100 yard dash can be calculated as:
Probability of Paul not winning = 7/9 ≈ 0.778 or 77.8%