Final answer:
The probability that Kristen's room number is divisible by 5 is 1/5, as there are 5 odd numbers divisible by 5 (15, 25, 35, 45, and 55) out of 25 total odd room numbers between 11 and 59.
Step-by-step explanation:
To calculate the probability that Kristen's room number is divisible by 5, we must first determine the total number of possible room numbers and then identify how many of these are divisible by 5. Since we are only considering odd room numbers from 11 through 59, we can list them as 11, 13, 15, ... , 57, 59. We can see that the sequence of odd numbers increases by 2 each time, starting at 11 and ending at 59.
To find the total count of odd numbers in this range, we use an arithmetic sequence formula: n = (last term - first term) / difference + 1, which gives us n = (59 - 11) / 2 + 1 = 25. So, there are 25 odd room numbers in total.
Now, to be divisible by 5, the last digit of the number must be either 5 or 0. However, since we are only considering odd numbers, the only possible last digit for a number divisible by 5 is 5. The odd room numbers that end with 5 are 15, 25, 35, 45, and 55. This gives us 5 numbers that meet the condition.
The probability that Kristen's room number is divisible by 5 is therefore the ratio of the number of favorable outcomes (numbers divisible by 5) to the total number of possible outcomes (total odd room numbers): probability = 5/25 = 1/5.