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 $3$?

Guest Nov 8, 2021

#1**0 **

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**

Guest Nov 9, 2021

edited by
Guest
Nov 9, 2021

#2**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__.

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

GA

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Guest 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

--. .-

Guest Nov 11, 2021