Final answer:
To find the probability of drawing a square number from a box of cards numbered 11 to 123, first determine the total number of cards in the box (113).
Then, find the total number of square numbers in the range (11). Finally, divide the number of square numbers by the total number of cards to find the probability (approximately 0.097).
Step-by-step explanation:
In this scenario, the box contains cards numbered from 11 to 123. We need to find the probability of drawing a square number. Square numbers are numbers that are the result of multiplying an integer by itself (e.g. 1, 4, 9, 16, etc.).
The first step is to identify the total number of cards in the box, which is found by taking the difference between the highest and lowest numbered cards and adding 1 (123 - 11 + 1 = 113).
The next step is to determine the total number of square numbers in the range. By taking the square root of the highest numbered card and rounding up to the nearest integer, we find that the highest square number is 11 (the square root of 123 is approximately 11.09).
Similarly, the lowest square number is 1 (the square root of 11 is approximately 3.32, so we round down). Thus, there are 11 - 1 + 1 = 11 square numbers in the range.
Finally, the probability of drawing a square number is found by dividing the number of square numbers by the total number of cards: 11/113 ≈ 0.097345. Therefore, the probability is approximately 0.097.