Probability of Rolling at Least One Six with Two Dice

In summary, the conversation discusses the probability of rolling at least one six when two dice are rolled. The solution involves finding the complement of the event "at least one is six" and using the principle of probability to determine the odds. The conversation also hints at the possibility of generalizing the principle to apply to a larger number of dice.
  • #1
XodoX
203
0

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).
 
Physics news on Phys.org
  • #2
What is the complement of the event "at least one is six"?
 
  • #3
0 six
 
  • #4
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?
 
  • #5
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.
 
  • #6
Alright. Thank you. I got it now.
 
  • #7
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?
 

FAQ: Probability of Rolling at Least One Six with Two Dice

1. What is the probability of rolling a specific number on two dice?

The probability of rolling a specific number on two dice is 1/36 or approximately 2.78%. This is because there are 36 possible outcomes when rolling two dice (6 possible outcomes for the first die and 6 possible outcomes for the second die) and only one of those outcomes will result in the specific number being rolled.

2. What is the probability of rolling a sum of 7 on two dice?

The probability of rolling a sum of 7 on two dice is 1/6 or approximately 16.67%. This is because there are 36 possible outcomes when rolling two dice and 6 of those outcomes will result in a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

3. What is the probability of rolling doubles on two dice?

The probability of rolling doubles on two dice is 1/6 or approximately 16.67%. This is because there are 36 possible outcomes when rolling two dice and 6 of those outcomes will result in doubles (1+1, 2+2, 3+3, 4+4, 5+5, 6+6).

4. Can the probability of rolling two dice be greater than 1?

No, the probability of rolling two dice cannot be greater than 1. The probability of an event is always a number between 0 and 1, where 0 means the event cannot occur and 1 means the event is certain to occur. Since it is impossible to roll a number greater than 12 on two dice, the probability can never be greater than 1.

5. How does the probability of rolling two dice change if one of the dice is loaded?

The probability of rolling two dice will change if one of the dice is loaded, as the loaded die will have a higher chance of landing on certain numbers. This can affect the overall probability of certain outcomes, such as rolling a specific number or rolling doubles. However, the exact change in probability will depend on how much weight is added to the loaded die and which numbers are affected.

Back
Top