Probability of Rolling at Least One Six with Two Dice

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Homework Help Overview

The problem involves calculating the probability of rolling at least one six when two dice are rolled. It also includes a variation where the probability is considered under the condition that the two faces are different.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the concept of complementary events and the probability of rolling no sixes. There are suggestions to consider simpler cases, such as rolling one die, to build understanding. Some participants propose a brute force method to enumerate possible outcomes.

Discussion Status

The discussion is active, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the use of complements and simpler cases, but no consensus has been reached on a final solution.

Contextual Notes

Participants are navigating the complexities of probability, particularly with the "at least one" condition and the implications of different scenarios involving the dice. There is an acknowledgment of the challenge posed by the problem's wording.

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Homework Statement


Two dice are rolled. What is the probability that at least one is six? If two faces are different, what is the probability that at least one is six?


Homework Equations





The Attempt at a Solution



I have no clue. Although the first one shouldn't be that hard, but it's "at least", so I don't really know. 1-P(0), I guess, but I'm not sure how to get P(0).
 
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What is the complement of the event "at least one is six"?
 
0 six
 
OK, so what's the probability of rolling two dice and getting no sixes?

If you're not sure about this, how about first answering the simpler question: what is the probability of rolling one die and getting no six?
 
Not that I recommend this but this problem is simple enough that you could solve it using brute force by writing all combos out. i.e. There are exactly 36 possible combinations of 2 dice. How many of those combinations contain at least one six?

Then, you can go back and generalize the principle that lead you to that answer.
 
Alright. Thank you. I got it now.
 
So, now that you know the principle, can you apply it? If you had 3 six sided dice, could you say the odds that at least one six turns up?
 

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