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