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# Two different natural numbers are selected from the set $\ \allowbreak \{1, 2, 3, \ldots, 6\}$. What is the probability that the greatest co

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Two different natural numbers are selected from the set $\ \allowbreak \{1, 2, 3, \ldots, 6\}$. What is the probability that the greatest common factor of these two numbers is one? Express your answer as a common fraction.

RektTheNoob  Sep 7, 2017

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Two different natural numbers are selected from the set

$$\{1, 2, 3, \ldots, 6\}$$.

What is the probability that the greatest common factor of these two numbers is one?

$$\begin{array}{|r|r|r|r|} \hline n & & \text{greatest common factor } = 1 & \text{greatest common factor } \ne 1 \\ \hline 1. & 5,6 & 1 \\ \hline 2. & 4,6 & & 2 \\ 3. & 4,5 & 1 \\ \hline 4. & 3,6 & & 3 \\ 5. & 3,5 & 1 \\ 6. & 3,4 & 1 \\ \hline 7. & 2,6 & & 2 \\ 8. & 2,5 & 1 \\ 9. & 2,4 & & 2 \\ 10. & 2,3 & 1 \\ \hline 11. & 1,6 & 1 \\ 12. & 1,5 & 1 \\ 13. & 1,4 & 1 \\ 14. & 1,3 & 1 \\ 15. & 1,2 & 1 \\ \hline & sum & 11 \\ \hline \end{array}$$

The probability is $$\mathbf{\tfrac{11}{15}}$$

heureka  Sep 7, 2017
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#1
+19207
+1

Two different natural numbers are selected from the set

$$\{1, 2, 3, \ldots, 6\}$$.

What is the probability that the greatest common factor of these two numbers is one?

$$\begin{array}{|r|r|r|r|} \hline n & & \text{greatest common factor } = 1 & \text{greatest common factor } \ne 1 \\ \hline 1. & 5,6 & 1 \\ \hline 2. & 4,6 & & 2 \\ 3. & 4,5 & 1 \\ \hline 4. & 3,6 & & 3 \\ 5. & 3,5 & 1 \\ 6. & 3,4 & 1 \\ \hline 7. & 2,6 & & 2 \\ 8. & 2,5 & 1 \\ 9. & 2,4 & & 2 \\ 10. & 2,3 & 1 \\ \hline 11. & 1,6 & 1 \\ 12. & 1,5 & 1 \\ 13. & 1,4 & 1 \\ 14. & 1,3 & 1 \\ 15. & 1,2 & 1 \\ \hline & sum & 11 \\ \hline \end{array}$$

The probability is $$\mathbf{\tfrac{11}{15}}$$

heureka  Sep 7, 2017

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