Probability of Rolling Sum > 8 w/ Dice: Calculating Probability & Avg Rolls

In summary, the probability for rolling a sum greater than 8 when rolling a pair of dice is 10/36. The conversation then discusses the probability of it taking two rolls to attain a sum greater than 8, with calculations using the equation (26/36)^(n-1) * (10/36). However, it is determined that this approach is not correct as the events are not independent. There is also a mention of the difficulty in considering rolling four dice at the same time.
  • #1
KingNothing
881
4
A pair of dice is being rolled. The probability for rolling a sum greater than 8 is 10/36.

Is the probability for it taking two rolls to attain a sum greater than 8 just 26/36 times 26/36?

I need to make a table of the number of rolls it takes to obtain a sum greater than 8, and the probability that it will take that many rolls. What equation do I use? Assume n is the number of rolls it takes.

EDIT: I think I figured it out as I was walking away from the comp. Is it (26/36)^(n-1) * (10/36)?

Assuming it is, how do you find the average number of rolls it takes to get that? It looks to be about 2.4. But how do I calculate that? Is it just 36/10 or 3.6?
 
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  • #2
KingNothing said:
Is the probability for it taking two rolls to attain a sum greater than 8 just 26/36 times 26/36?

Umm...but the thing is...I interpret the sentence "the probability that it will take two rolls to attain a sum > 8" to mean that you actually get a sum greater than 8 on the second roll. Otherwise, it would take 3 or more rolls! So why did you multiply by 26/36 the second time?

In general, I am not sure about the strategy of multiplying the probabilities together. Wouldn't you expect the probability of obtaining a sum > 8 to increase with larger n? Yet, if you multiply the probabilities, the product only gets smaller.

Yeah, they are not independent events, because if you consider the events independent and multiply the probabilities together (using your formula)...you are calculating the chances of getting a sum less than eight exactly n-1 times, followed by a sum > 8 the nth time. So that's NOT the way to do it.

I'll have to think about it more. No doubt somebody will explain how to do it before I figure it out.
 
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  • #3
when you said you roll two times... how is it differ from rolling 4 dices at the same time? ... hope this answer your question...
 
  • #4
vincentchan said:
when you said you roll two times... how is it differ from rolling 4 dices at the same time? ... hope this answer your question...

It just makes it more complicated to think of rolling four dice and dealing with sums greater than 8.
 
  • #5
what grade r u in?
 
  • #6
Is the probability for it taking two rolls to attain a sum greater than 8 just 26/36 times 26/36?

are u saying the sum of two rolls is greater than 8, or both rolls is greater than 8?
 

FAQ: Probability of Rolling Sum > 8 w/ Dice: Calculating Probability & Avg Rolls

What is the probability of rolling a sum greater than 8 with two dice?

The probability of rolling a sum greater than 8 with two dice is 21/36 or approximately 58.33%. This can be calculated by first finding the total number of possible outcomes, which is 36 (6 possible outcomes for the first die multiplied by 6 possible outcomes for the second die). Then, we need to find the number of outcomes that result in a sum greater than 8, which is 21 (7 possible outcomes for the first die multiplied by 3 possible outcomes for the second die, plus 6 possible outcomes for the first die multiplied by 2 possible outcomes for the second die).

How can we calculate the probability of rolling a sum greater than 8 with three dice?

The probability of rolling a sum greater than 8 with three dice can be calculated by first finding the total number of possible outcomes, which is 216 (6 possible outcomes for each of the three dice). Then, we need to find the number of outcomes that result in a sum greater than 8, which is 120 (10 possible outcomes for the first die multiplied by 10 possible outcomes for the second die, plus 15 possible outcomes for the first die multiplied by 6 possible outcomes for the second die, plus 20 possible outcomes for the first die multiplied by 3 possible outcomes for the second die).

How many rolls, on average, will it take to get a sum greater than 8 with two dice?

On average, it will take approximately 2.73 rolls to get a sum greater than 8 with two dice. This can be calculated by dividing the total number of possible outcomes (36) by the number of outcomes that result in a sum greater than 8 (21).

Is the probability of rolling a sum greater than 8 with two dice affected by the order of the dice?

No, the probability of rolling a sum greater than 8 with two dice is not affected by the order of the dice. This is because the total number of possible outcomes and the number of outcomes that result in a sum greater than 8 remains the same, regardless of the order in which the dice are rolled.

How can we use this probability to make informed decisions in games or real-life situations?

Knowing the probability of rolling a sum greater than 8 with two dice can help us make informed decisions in games or real-life situations. For example, in a game of craps, understanding this probability can help us decide which bets to make. In real-life situations, this knowledge can be useful in estimating the likelihood of certain outcomes, such as rolling a specific number on a pair of dice in a board game or rolling a certain sum in a game of Yahtzee.

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