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## Comment on

4-Digit Number## don't you think the 2nd, 3rd

## No, it's still 1/10 (although

No, it's still 1/10 (although it certainly seems like it might be 1/9).

However, it doesn't matter that the 1st value can't be 0. There are 10 possible values for the 2nd digit, and only 1 of them matches the 1st digit. So, the probability that the 2nd number matches the first is 1/10

## For probability approach: Why

## We're selecting an integer

We're selecting an integer from 1000 to 9999, so it's impossible for the 1st digit (the thousands digit) to be zero.

## Can we imply that the

## Yes, that would be an

Yes, that would be an equivalent model.

Great idea!

## Why isn't the probability of

## The first digit can be ANY

The first digit can be ANY digit among 1, 2, 3, 4, 5, 6, 7, 8, and 9

It doesn't matter which digit it is. What matters is that the remaining digits match the first digit.

Does that help?

## Why is the probability of the

## If we want all 4 digits to be

If we want all 4 digits to be the same, then it doesn't matter what the first digit is.

For example, if the first digit is a 7 then, in order for all 4 digits to be the same, we need the other three digits to be 7.

Similarly, if the first digit is a 9 then, in order for all 4 digits to be the same, we need the other three digits to be 9.

If the first digit is a 2 then, in order for all 4 digits to be the same, we need the other three digits to be 2.

So, the likelihood of all 4 digits being the same does not depend on the value of the first digit.

In fact, the first digit can be ANY digit.

If we randomly choose a digit to be the first digit, what is the probability that the selected digit is ANY digit?

Since our first selection is guaranteed to be an integer, the probability is 1.

Does that help?

Cheers,

Brent

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