Final answer:
The probability that a 2-digit number between 50 and 99 is divisible by 6 is 4/25, as there are 8 numbers divisible by 6 in this range out of a total of 50 numbers.
Step-by-step explanation:
To find the probability that a 2-digit number chosen at random between 50 and 99 is divisible by 6, we first identify those numbers within the range that are divisible by 6. Starting with 54 (the first 2-digit number after 50 that is divisible by 6) and ending with 96, the numbers divisible by 6 in this range are 54, 60, 66, 72, 78, 84, 90, and 96. There are a total of 8 numbers.
Next, we determine the total number of 2-digit numbers between 50 and 99. Since each digit from 50 to 99 is distinct, there are 99 - 50 + 1 = 50 numbers in total.
The probability is then the number of favorable outcomes (numbers divisible by 6) divided by the total number of possible outcomes (total number of 2-digit numbers from 50 to 99). Thus, the probability = 8 / 50 = 4 / 25.