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 $3$?
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
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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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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