What is the probability that an integer x:(1<x<30) chosen at random is divisible by both 2 and 3?
To find the probability that an integer between 1 and 30 is divisible by both 2 and 3, we need to find the common multiples of 2 and 3 between 1 and 30.
The common multiples of 2 and 3 are numbers that are multiples of both 2 and 3, which means they are multiples of the least common multiple of 2 and 3, which is 6.
The common multiples of 2 and 3 between 1 and 30 are 6, 12, 18, and 24.
There are 4 common multiples of 2 and 3 between 1 and 30.
Therefore, the probability that an integer between 1 and 30 is divisible by both 2 and 3 is 4/30 = 2/15.