Home / Expert Answers / Statistics and Probability / what-is-the-probability-that-a-4-digit-number-a-starts-with-a-3-b-is-a-multiple-of-5-c-starts-pa741

# (Solved): what is the probability that a 4 digit number: a. Starts with a 3? b. Is a multiple of 5? c. Starts ...

what is the probability that a 4 digit number: a. Starts with a 3? b. Is a multiple of 5? c. Starts and ends with a 3?

We have an Answer from Expert

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%.

We have an Answer from Expert