Final answer:
To find the probability that a randomly chosen 4-digit number with exactly one digit as 7, leaves a remainder of 2 when divided by 5, we need to determine the favorable outcomes and the total number of outcomes. The probability is 1/9. The correct answer is B. 2/9.
Step-by-step explanation:
To find the probability that a randomly chosen 4-digit number with exactly one digit as 7, leaves a remainder of 2 when divided by 5, we need to determine the favorable outcomes and the total number of outcomes. The favorable outcomes are the 4-digit numbers that end with 7 and leave a remainder of 2 when divided by 5. The total number of outcomes is the total number of 4-digit numbers with exactly one digit as 7.
Let's break it down:
- The last digit must be 7. There are 9 possible digits (0-9), but since it cannot be 7 itself, there are 8 possibilities.
- The first three digits can be any digit from 0-9 (except 7), giving us 9 x 10 x 10 = 900 possibilities.
Therefore, the total number of outcomes is 8 x 900 = 7200.
The number of favorable outcomes is the number of 4-digit numbers that end with 7 and leave a remainder of 2 when divided by 5. The only possible last digit is 7. The first three digits can be any digit from 0-9 (except 7). The remaining two digits can be any digit from 0-9.
Therefore, the number of favorable outcomes is 8 x 10 x 10 = 800.
The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Favorable outcomes / Total outcomes = 800 / 7200 = 1/9 = 0.1111