Q: What is the probability that a 3-digit number has an even digit in the hundreds place?

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875

The smallest 3 digit counting number less than 1000?? 100

The digit in the hundreds place in the number 2378.91 is the digit 3.

285

3

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875

The smallest 3 digit counting number less than 1000?? 100

The digit in the hundreds place in the number 2378.91 is the digit 3.

The digit in the hundreds place in the number 463 is the digit 4.

285

3

1339

The digit of 0 represents the hundreds place

The probability is 1/2.

The probability is 1/2.

216.

For me I think it is conceptually easier to think about the probability that the number will contain the digit seven (and the probability that it does not contain the digit 7 is simply one minus the probability that it does). P(number will contain 7) = P(number is in the seven hundreds) + P(number is not in seven hundreds)*[P(number is in the X hundred seventies)+P(number is not in the X hundred seventies)*P(number ends in seven)] So essentially I am considering all of the numbers in the range that start with seven (i.e., are in the seven hundreds), then all of the numbers in the range that aren't in the seven hundreds but have a 7 in the tens place (i.e., the 170s, 270s, etc., and finally all the numbers that don't have a 7 in the hundred or tens place, but that end in 7). Plugging the numbers into my formula above, I get (100/900)+(800/900)*((10/100)+(90/100)(1/10)) = 7/25 is probability that the number does contain a 7, and 1-(7/25)=18/25 is probability that it does not.