Final answer:
The probability that Troy's card is a multiple of 5 or a multiple of 9 is 7/25 or 28%.
Step-by-step explanation:
The sample space consists of twenty-five cards labeled 1 through 25.
Troy randomly selects one card from the bag, which means that there is only one favorable outcome. To calculate the probability, we need to determine the number of favorable outcomes (cards that are multiples of 5 or multiples of 9) and divide it by the total number of possible outcomes (25 cards). To find the number of favorable outcomes, we need to find the multiples of 5 and the multiples of 9 within the range of 1 to 25. The multiples of 5 are 5, 10, 15, 20, and 25. The multiples of 9 are 9, 18, and 25. Since 25 is a common multiple, we need to count it only once. Therefore, the number of favorable outcomes is 7. The probability that Troy's card is a multiple of 5 or a multiple of 9 can be calculated as 7/25, which simplifies to 0.28 or 28%.