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# Probability

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Wu rolls two fair six-sided dice.  You are not told what the rolls were, but you are told that the sum of the two rolls is a prime.  What is the probability that the sum of the two rolls is $3$?

Nov 8, 2021

#1
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These are all the ways of summing up 2 dice:

(2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12)>>Total = 36

In how many ways can you make up a 3? Only in 2 ways:(1, 2) and (2,1):

Count ALL the prime numbers that you can make on a roll 2 dice. Just count all the primes from the above list and you should get 15:

Therefore, the probability of rolling a "3" out of 15 primes is: 2 / 15

Nov 9, 2021
edited by Guest  Nov 9, 2021
#2
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This is NOT the correct solution for the question asked.

We are told two rolled-dice sum to a prime.  How the dice roll to produce this prime sum is irrelevant.

Equivalent restatement of question:

Given that the sum of two numbers on fairly-rolled dice is a prime number, what is the probability that the sum is three (3)?

Solution:

Calculate the Relative Probabilities of its occurrence by weighting the occurrence of each possible prime by its Absolute Probability.

$$\begin{array}{|rccc|} \hline & Sum &\text {Absolute Probability} &\text{Relative Probability }\\ &2 &2.78\% &6.67\% \\ &3 &5.56\% &13.34\% \\ &5 &11.11\% &26.67\% \\ &7 &16.67\% &40.00\% \\ &11 &5.56\% &13.34\% \\ \hline \end{array}\\ \text{ }\\ \hspace{16em}\; \;\text {The probability is } \mathrm {13.34\%}\\$$

GA

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Nov 9, 2021
#3
0

This is NOT the correct solution for the question asked.

We are told two rolled-dice sum to a prime.  How the dice roll to produce this prime sum is irrelevant.

Equivalent restatement of question:

Given that the sum of two numbers on fairly-rolled dice is a prime number, what is the probability that the sum is three (3)?

Solution:

Calculate the Relative Probabilities of its occurrence by weighting the occurrence of each possible prime by its Absolute Probability.

$$\begin{array}{|rccc|} \hline & Sum &\text {Absolute Probability} &\text{Relative Probability }\\ &2 &2.78\% &6.67\% \\ &3 &5.56\% &13.34\% \\ &5 &11.11\% &26.67\% \\ &7 &16.67\% &40.00\% \\ &11 &5.56\% &13.34\% \\ \hline \end{array}\\ \text{ }\\ \; \;\text {The probability is } \mathrm {13.34\%}\\$$

GA

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Nov 11, 2021