### Brain Teasers

# The Lottery

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

Consider a very simple weekly lottery: A number between one and one million (inclusive) is randomly chosen each week.

1. If you play one number this week, what are your odds of winning?

2. If you won this week, what are the odds of you winning by choosing the same number next week?

3. If you won this week, what are the odds of you winning by choosing a different number next week?

4. What are the odds of the winning number being 50, two weeks in a row?

5. What are the odds of the winning number being the same, two weeks in a row?

1. If you play one number this week, what are your odds of winning?

2. If you won this week, what are the odds of you winning by choosing the same number next week?

3. If you won this week, what are the odds of you winning by choosing a different number next week?

4. What are the odds of the winning number being 50, two weeks in a row?

5. What are the odds of the winning number being the same, two weeks in a row?

### Answer

1. Since there are a million possible numbers, the odds of winning are 1:1 million.2 & 3. Since you already won this week, that does not need to be taken into consideration for next week. Your odds of winning are still 1:1 million no matter what number you choose, even if it was last week's winning number.

4. The odds of the number 50 coming up in each week are 1:1 million. Combining the two weeks, you multiply 1:1 million by 1:1 million to get 1:1 trillion.

5. Since for the first week the number doesn't matter, you only have to consider the second week. The odds of getting the first week's winning number in the second week are the same as the odds of getting any other number, or 1:1 million.

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