Question

Consider all four-digit numbers that can be created from the digits 0.9 where the first and last digits must be odd and no digit can repeat. What is the probablity of choosing a random number that starts with 7 from this group?

Answer 1

To find the probability of choosing a random number that starts with 7, determine the total number of possible numbers and the number of numbers that start with 7. The probability is 1/5 or 0.2.

Step-by-step explanation:

To find the probability of choosing a random number that starts with 7 from the given group, we need to determine the total number of possible numbers and the number of numbers that start with 7.

Since the first and last digits must be odd and no digit can repeat, there are 5 choices for the first and last digit (1, 3, 5, 7, 9), and for the two middle digits, there are 8 choices for each.

Therefore, the total number of possible numbers is 5 * 8 * 8 * 5 = 1600.
Out of these, the number of numbers that start with 7 is 8 * 8 * 5 = 320.

So, the probability of choosing a random number that starts with 7 is 320 / 1600 = 1/5 or 0.2.