a natural number is chosen at random from among the first 500. what is the probability that the number chosen is divisible by 3 or 5

233/500
This may not be the textbook method, but it sure works:
Number of possible outcomes for a number…
Divisible by 5: 500 / 5 = 100 numbers
Divisible by 3: 500 / 3 = 166.66 ≈ 166 numbers
Divisible by both 3 and 5 (i.e. 15): 500 / 15 = 33.33 ≈ 33 numbers
Divisible by either 3 or 5: (100 + 166) – 33 = 233 numbers
Probability the number chosen being divisible by 3 or 5: 233 / 500