### Brain Teasers

# The Lottery

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

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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## Comments

Feb 28, 2003

pretty interesting but a easy sip to the lip

boring!

Great to have you back, mogmatt.

Very easy! I thought that there'd be a twist to it.

I agree

I have to admit you are very good at making puzzles you are a geinus so good job!

Quick note on notation -- the Probability is 1/1,000,000. The Odds are 999,999:1. (Obviously changes for the 1/1Trillion...) Probability is denoted as (success)/(success + failure), whereas odds are denoted as (failure)success).

very nice.

As stated, the answers for 4 and 5 are wrong. The questions the author answered are "What are the chances that the winning number will be (50 / the same) this week and next.

By not putting a time frame on it, what he really asked was: "What are the chances that the winning number will be (50 / the same) two weeks in a row **EVER**?" The answer is that it is a certainty that, some time between now and infinity, we well see the same number twice in a row. Also, some time between now and infinity we will see the number 50 win twice in a row.

By not putting a time frame on it, what he really asked was: "What are the chances that the winning number will be (50 / the same) two weeks in a row **EVER**?" The answer is that it is a certainty that, some time between now and infinity, we well see the same number twice in a row. Also, some time between now and infinity we will see the number 50 win twice in a row.

Zag, what is the probability that that would happen? I see. You misunderstood the question.

odds* not probability : (

I liked this one, I got fooled into multiplying weeks one and two, didn't pay attention to the wording!

got prankt

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