Calculating Probability: Sum of 79 Rolls and Exceeding 300

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SUMMARY

The discussion centers on calculating the probability that at least 80 rolls of a fair die are necessary for the sum to exceed 300. The key conclusion is that this scenario is equivalent to determining the probability that the sum of 79 rolls is less than or equal to 300. The confusion arises from the interpretation of the phrase "at least 80 rolls," which includes the possibility of rolling more than 80 times if the sum of the first 79 rolls does not exceed 300.

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AKBAR
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I'm confused about this question.

The problem: The sum of the rolls of a fair die exceed 300. Find the probability that at least 80 rolls were necessary.

The solution we were given is that this event is equivalent to the sum of 79 rolls being less than or equal to 300. But I don't get it. The sum of 79 rolls could be 79, assuming you rolled a one every time. Then the 80th roll would not exceed 300. There are plenty of cases of the sum of 79 rolls being less than 300 where the 80th roll would not exceed 300. Can anyone help explain this to me?

Thanks!
 
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AT LEAST 80 rolls. That means 80 or MORE. Your example has more than 80 rolls. So it is at least 80 rolls.
 

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