# what is the probability that a random number generator generates a 3 digit number where the 1st digit is prime and the number is multiple of ten

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Expert Answers

samhouston | Certified Educator

The first digit is prime, so the choices are:

2, 3, 5, and 7

There are no restrictions on the second digit, so the choices are:

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

The number is a multiple of 10, so the third digit must be:

0

To find the number of 3-digit numbers that meet the above criteria, multiply the number of choices for each digit.

First digit: 4 choices

Second digit: 10 choices

Third digit: 1 choice

4 * 10 * 1 = 40

With no restrictions, there are 1,000 possible combinations.

10 * 10 * 10 = 1,000

The probability will be 40 out of 1,000.

**Answer: 40/1,000 = 0.04 = 4%**