### Brain Teasers

# My Lucky World Series

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability

Before the beginning of the baseball season, a certain Las Vegas casino listed the odds for my favorite National League team making it to the World Series as 11:1.

The same casino listed odds that made my favorite American League twice as likely as my favorite National League team of making it to the World Series.

Additionally, if either one of my favorite teams makes it to the World Series, it has even odds of winning the Series.

Assuming the chance of an NL team making it to the World Series is independent of the chance of an AL making it to the World Series, what are the odds, as given by the casino, that one of my favorite teams becomes World Champions?

The same casino listed odds that made my favorite American League twice as likely as my favorite National League team of making it to the World Series.

Additionally, if either one of my favorite teams makes it to the World Series, it has even odds of winning the Series.

Assuming the chance of an NL team making it to the World Series is independent of the chance of an AL making it to the World Series, what are the odds, as given by the casino, that one of my favorite teams becomes World Champions?

### Hint

The odds given by a casino are called house odds, which give the odds AGAINST an event occurring.For example, the casino's odds of 5:2 means the odds against that event occurring is 5 to 2, giving the event a 2/7 probability of occurring.

### Answer

7:1 (1/8 probability).Since my National League team is listed at 11:1, then the probability of them making the World Series is 1/12. My American League team, being twice as likely of making it to the Series, would have a probability of 1/6 (5:1).

Let A = probability of AL team winning and N= probability of NL team winning. Then P(A or N) = P(A) + P(N).

P(A) = 1/6 x 1/2 = 1/12; P(N) = 1/12 x 1/2 = 1/24 .

Thus, P(A or N) = 1/12 + 1/24 = 1/8. Hence, the odds of one of my favorite teams winning the World Series would be listed at 7:1.

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