A number is chosen at random from the set 1, 2, 3, ..., 103. What is the probability that the number is from the set G=x : 4 < x < 8?

The numbers are chosen from the set $\{1, 2, 3, \dots, 103\}$.
The total number of possible outcomes is the count of numbers in this set, which is 103.

The favorable outcomes are numbers $x$ such that $4 < x < 83$. Since $x$ must be an integer, the numbers in this range are $5, 6, 7, \dots, 82$.

To find the number of integers between two values (exclusive), subtract the smaller value from the larger value and then subtract 1.
Number of favorable outcomes $= 82 - 5 + 1 = 77 + 1 = 78$.

The probability $P$ is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.

The probability is $\frac{78}{103}$.