Final answer:
The probability of the team winning the championship game is 0.7, calculated from the given odds against of 3:7 by adding the numbers in the odds ratio and dividing the number of favorable outcomes by the total number of possible outcomes.
Step-by-step explanation:
The odds against a team winning are given as 3:7.
To find the probability of the team winning, we must understand that odds against and probability are related but not the same.
Odds of 3:7 against winning mean that for every 3 scenarios where the team loses, there are 7 scenarios where the team wins.
To calculate the probability of winning, we add together the two numbers in the odds ratio to get the total number of possible outcomes, which is 3 (losses) + 7 (wins) = 10 total possible outcomes.
The probability of winning is the number of favorable outcomes (wins) divided by the total number of possible outcomes.
Therefore, the probability is 7/10 or 0.7.