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Here is answer-

To calculate the probability for each scenario, we need to consider the total number of possible outcomes and the number of favorable outcomes that satisfy the given conditions.

a. Probability that a 4-digit number starts with a 3:

There are a total of 9,000 4-digit numbers (ranging from 1000 to 9999). Out of these, the numbers starting with 3 range from 3,000 to 3,999, which includes 1,000 possible numbers.

Probability = Number of favorable outcomes / Total number of outcomes Probability Probability = 1/9 or approximately 0.1111

Therefore, the probability that a randomly chosen 4-digit number starts with a 3 is approximately 0.1111 or 11.11%.

Here's a more detailed explanation for each scenario:

Probability that a 4-digit number starts with a 3:

To calculate this probability, we need to determine the number of 4-digit numbers that start with 3 and divide it by the total number of 4-digit numbers.

In the range of 4-digit numbers (from 1000 to 9999), numbers that start with 3 range from 3000 to 3999. There are 1000 numbers that satisfy this condition.

The total number of 4-digit numbers is 9999 - 1000 + 1 = 9000.

Therefore, the probability that a randomly chosen 4-digit number starts with a 3 is 1000/9000 = 1/9 ? 0.1111 or approximately 11.11%.