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The actual problem is stated as follows:

The chance of getting hit by lightning is 1 in 600,000. In the lottery you will play, you'll chose 6 numbers out of the first 30. Do you have a better chance of getting hit by lightning or winning the lottery?

To me, I feel like this problem is ambiguous and has left out some needed things. For example, wouldn't we need to know the total population when trying to find the chance of getting hit by lightning? And for the lottery wouldn't we need some more information as well?

My first thought was that this is an unanswerable question. If this is true, could I just make up some arbitrary numbers? And if I can, what would that look like in this case?

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  • $\begingroup$ Ignore the lightning part for now. Can you compute the probability of winning the lottery? $\endgroup$ Jun 14, 2016 at 16:20
  • $\begingroup$ No, making up arbitrary numbers is not feasible. What if you decide that the population is $1,000,000,000,000,000$? But, making estimates might be allowable, if they can be realistically justified. Maybe one of those events is so much less likely than the other that realistic estimates will demonstrate it. $\endgroup$
    – Lee Mosher
    Jun 14, 2016 at 16:21

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The problem isn't ambiguous, just not worded terribly well. The given probability of being struck by lightning assumes some information about frequency of lightning strikes, population, exposure to risk, and so on. You are to assume the probability that you will, at some point, be struck by lightning is $\frac{1}{600000}$.

With that said, can you compute the probability that you win the lottery? Similarly poor wording here, but you are to assume that only matching all six numbers wins, and it is safe to assume numbers may not be repeated (implicit in colloquial use of "lottery").

How many possible choices of six numbers are there? How many such choices will match a winning set of six given numbers?

Once you know the answers to these two questions, you can compute the probability you win this lottery, then answer the real question, which is:

Is the probability of choosing a particular set of six integers between $1$ and $30$ greater than, equal to, or less than $\frac{1}{600000}?$

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