Final answer:
The probability of selecting a positive integer divisible by 4 from the set of positive integers not exceeding 60 is approximately 0.9667.
Step-by-step explanation:
To find the probability of a positive integer selected at random from the set of positive integers not exceeding 60 to be divisible by 4, we need to determine the number of positive integers in this set that are divisible by 4 and divide it by the total number of positive integers not exceeding 60.
Divisible by 4:
4, 8, 12, 16, ..., 60
The difference between consecutive numbers in this list is 4, so we can use the formula for finding the number of terms in an arithmetic sequence to calculate the number of positive integers divisible by 4:
a = 4, d = 4 (common difference), l = 60
n = (l - a)/d + 1
n = (60 - 4)/4 + 1 = 57/4 + 1 = 58.75
However, since we are considering only positive integers not exceeding 60, we round down to the nearest whole number, which is 58.
The total number of positive integers not exceeding 60 is 60. Therefore, the probability of selecting a positive integer divisible by 4 is 58/60 = 0.9667 (rounded to four decimal places).