My locker combination has three digits. None of the digits are 0. What is the probability that the first digit of my locker combination is greater than 6?
3 digits greater than 6 ... 7 , 8 , 9
3 possible digits out of 9 (no zero)
Thank you for your help
To find the probability that the first digit of your locker combination is greater than 6, we first need to determine the total number of possible combinations and then count how many of them have a first digit greater than 6.
Since your locker combination has three digits, and none of them can be 0, we know that each digit has 9 possible choices (1-9). Therefore, the total number of possible combinations is 9 * 9 * 9 = 729.
Now, let's determine how many combinations have a first digit greater than 6. Since the first digit can only be 7, 8, or 9 (greater than 6), we have three choices for the first digit. For the remaining two digits, each of them can be any digit from 1 to 9, so we have 9 choices for each of the second and third digits.
Therefore, the number of combinations with the first digit greater than 6 is 3 * 9 * 9 = 243.
Finally, to find the probability, we divide the number of favorable outcomes (combinations with the first digit greater than 6) by the total number of possible outcomes (total combinations):
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 243 / 729 = 1 / 3 ≈ 0.333 (or 33.3% when rounded to the nearest percent).
So, the probability that the first digit of your locker combination is greater than 6 is approximately 0.333 or 33.3%.