Probability of throwing a 6 in dice

In summary, the conversation discusses the probability of getting more than 100 sixes when throwing a dice 20 times. The speaker suggests using the Negative Binomial Distribution instead of the Binomial Distribution and explains that the desired probability is the probability of having less than 20 sixes after 100 dice throws.
  • #1
Dell
590
0
i throw a dice until i get a result (6) 20 times, what is the probability that i will throw the dice more than 100 times?

i made X=amount of times i throw the dice

so now I am looking for P(X>100)

i think that i can say X~B(n, 1/6)
but the problem is that i don't know n, since it is anything over 100
 
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  • #3
http://en.wikipedia.org/wiki/Geometric_distribution"
 
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  • #4
In this problem you can always throw the dice 100 times. If you get 20 or more sixes, you needed to throw the dice 100 times or less to get exactly 20 sixes. If you haven't reached 20 yet, then that means that you would have reached 20 had you thrown the dice more than 100 times.

So, the desired probability is the probability that after 100 dice throws you have less than 20sixes.
 
  • #5
thanks, that's great
 

1. What is the probability of throwing a 6 on a single die?

The probability of throwing a 6 on a single die is 1/6 or 16.67%. This is because there are six possible outcomes on a single die (1, 2, 3, 4, 5, 6) and only one of those outcomes is a 6.

2. What is the probability of throwing a 6 on two dice?

The probability of throwing a 6 on two dice is 11/36 or 30.56%. This is because there are 36 possible outcomes when rolling two dice, and 11 of those outcomes include at least one 6 (1+6, 2+6, 3+6, 4+6, 5+6, 6+1, 6+2, 6+3, 6+4, 6+5, 6+6).

3. How does the number of dice rolled affect the probability of throwing a 6?

The more dice that are rolled, the higher the probability of throwing a 6. For example, when rolling three dice, the probability of throwing a 6 is 91/216 or 42.13%. This is because there are more possible combinations that include at least one 6 (1+6+6, 2+6+6, 3+6+6, 4+6+6, 5+6+6, 6+1+6, 6+2+6, 6+3+6, 6+4+6, 6+5+6, 6+6+1, 6+6+2, 6+6+3, 6+6+4, 6+6+5, 6+6+6).

4. Is the probability of throwing a 6 affected by the order of the dice?

No, the probability of throwing a 6 is not affected by the order of the dice. Whether you roll a 6 on the first, second, or third die, the probability remains the same. Each die has an equal chance of rolling a 6.

5. How does the probability of throwing a 6 change if there is a loaded die?

If there is a loaded die, the probability of throwing a 6 will be higher or lower depending on the weight distribution of the die. A loaded die with more weight on the 6 side will have a higher probability of rolling a 6, while a loaded die with less weight on the 6 side will have a lower probability of rolling a 6. It is important to note that using a loaded die is considered cheating and can affect the fairness of the game.

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