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# Conditional probability

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Four fair 6-sided dice are rolled. The sum of the numbers shown on the dice is 8. What is the probability that 2's were rolled on all four dice?

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I have tried finding the total number of ways, but to no avail. Can i have som help?

Max0815  Aug 31, 2018
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anyone can help?

Max0815  Sep 1, 2018
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The probability of rolling 4 dice and getting 4 twos is:

1/6 x 1/6 x 1/6 x 1/6 =1/1,296 =0.0007716

Guest Sep 1, 2018
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@above, sorry, but your response is incorrect, because you didnt account for the conditions...thats why it was titled conditional probability lol xD! I know that your answer is right without conditions, but how do i do it with these conditions??? ANyone help???

Max0815  Sep 1, 2018
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There are 5 ways of getting a total of 8 on a roll of 4 dice and each has the following number of prmutations:
5 + 1 + 1 + 1 = 8=4!/3! =4 permutations
4 + 2 + 1 + 1 = 8=4!/2!=12 permutations
3 + 3 + 1 + 1 = 8=4!/2!. 2!=6 permutations
3 + 2 + 2 + 1 = 8=4!/2!=12 permutations
2 + 2 + 2 + 2 = 8=4!/4!=1 permutation
4 + 12 + 6 + 12 + 1 = 35 ways of getting a total of 8. And only 1 of them is 4 twos. Therefore, the probability of throwing 4 twos given a total of 8 is:
1/35 =0.028571.

Guest Sep 1, 2018
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Ginger, aren’t you going to troll this post?

Guest Sep 1, 2018
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Patients! Goddamn it!

Writing a good troll post isn’t as easy as solving probability problems.

GingerAle  Sep 1, 2018
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The number of permutations for screwing up a simple statistics question is truly mind boggling. I’ve always wondered what the number actually is. It may not actually have a ceiling --it seems as vast as space, and the time to do it is limited only by the imagination and cogitative lifespan of humankind.

GA

GingerAle  Sep 1, 2018
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This was worth waiting for!

Guest Sep 1, 2018
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Solution:

The sum of four (4) dice is eight (8).

There are five (5) ways to roll four (4) dice for a sum of eight (8).

5, 1, 1, 1

4, 2, 1, 1

3, 3, 1, 1

3, 2, 2, 1

2, 2, 2, 2

One of these five (5) are four (4) twos (2).

The probability is 1/5 = 20%

GA

GingerAle  Sep 1, 2018
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What does this answer mean?

https://www.wolframalpha.com/input/?i=4+dice+rolled,+probability+of+total+of+8

Guest Sep 1, 2018
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It’s very easy to tell you what this means.

This means you know how to ask a computer a question, but not the correct question.

WolfRam correctly answered the question you asked.

You need to ask it this conditional question: Four (4) dice sum to eight (8). What’s the probability the four (4) dice are all twos (2).

If you phrase this correctly, WolfRam wil answer it correctly.

GA

GingerAle  Sep 1, 2018
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The probability of an event A occuring given that another event B occured is given by the probability that both events occur divided by the probability that event B occurs.

in this question, A=the event where 2's were rolled on all four dice, and B=the event when the sum of the numbers shown on the dice is 8.

the probability of both events occuring is simply the probability that after rolling, the faces of all dice show 2, which is 1 divided by 64=$$\frac{1}{1296}$$

In the link the guest provided, wolfram alpha gives the final answer of $$\frac{35}{1296}$$, so the probability that after rolling the dice, the sum of the numbers on their faces is 8 is 35 divided by 1296

Finally, to find the probability of event A occuring given that event B occured, we have to divide 1/1296 by 35/1296:

$$\frac{\frac{1}{1296}}{\frac{35}{1296}}=\frac{1}{35}$$

so the probability is 1/35

Guest Sep 1, 2018
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I agree with the 2 guests.

I believe that the answer is   1/35

I did it the same way as the first guest.

Ginger you did not take into consideration the number of permutaions for each set of outcomes. You have to think of the 5 dice as all being different from each other.

Melody  Sep 1, 2018