My locker combination has three digits. None of the digits are zero. What is the probability that the first digit of my locker combination is less than 4?
There are 3 possible digits less than 4
so prob = 3/9 = 1/3
To find the probability that the first digit of your locker combination is less than 4, we need to determine the total number of possible combinations and the number of combinations that meet the given condition.
Since the combination consists of three digits, each digit can have 10 possible values (0-9) except for the first digit, which cannot be zero. Therefore, the total number of possible combinations is 9 * 10 * 10 = 900.
Now, let's determine the number of combinations where the first digit is less than 4. The first digit can take on the values 1, 2, or 3. For the second and third digits, each can be any of the 10 possible values (0-9).
So, the number of combinations where the first digit is less than 4 is 3 * 10 * 10 = 300.
Therefore, the probability that the first digit of your locker combination is less than 4 is 300/900, which simplifies to 1/3 or approximately 0.3333.