+0

# Help Probability!

+1
157
2
+314

Two integers are relatively prime if they have no common factors other than 1 or -1. What is the probability that a positive integer less than or equal to 30 is relatively prime to 30? Express your answer as a common fraction.

Jul 8, 2018

#1
-1

$${7 \over 29}$$

.
Jul 8, 2018
#2
+1

Since 30 = 2 x 3 x 5, therefore it has common factors with the following numbers:
2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30[22 numbers]
It is relatively prime with following numbers:
1, 7, 11, 13, 17, 19, 23, 29[8 numbers]
Therefore, the probability that a number =< 30 is relatively prime to 30 is:
8 / 30 = 4 / 15

Jul 8, 2018