You pick 2 digits (0-9) at random without replacement, and write them in the order picked.
What is the probability that you have written the first 2 digits of your phone number? Assume there are no repeats of digits in your phone number.
Give your answer as a fraction.
To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since we are picking 2 digits without replacement from a set of 10 digits (0-9), there are 10 choices for the first digit and 9 choices for the second digit. Therefore, the total number of possible outcomes is 10 * 9 = 90.
Now, let's determine the number of favorable outcomes. Assuming you have a standard phone number that has 10 digits in total and no repeats, the first two digits of your phone number can be any two digits from the remaining eight digits (after the first digit is already fixed). Therefore, there are 8 choices for the first digit of your phone number (excluding the digit already picked) and 7 choices for the second digit. So, the number of favorable outcomes is 8 * 7 = 56.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
= 56 / 90
Therefore, the probability that you have written the first 2 digits of your phone number is 56/90, which can be simplified further if needed.