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## Karl Proposes a Probability Question. Risky!

Posted by Karl Sharman on January 8, 2011 – 12:10 pm

If we consider 2-digit numbers, there are exactly 18 numbers that contain the digit one: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91

As there are ninety 2-digit numbers, the probability of a 2-digit number containing a one is 18/90 = 1/5. If I have got this wrong, then the answer I have is wrong, and some one better tell me fairly quickly so I can remove the problem!

What proportion of 3-digit numbers contain the digit one?

This post is under “Tom” and has 11 respond so far.

### 11 Responds so far- Add one»

1. 1. Curtis Said：

seems to be 28%

900 3 didit nos. 100-999

all 100-199 =100

the 18 mentioned above for each 200-900 =144

and also 201, 301…..901 =8

total 252/900 = 28%

2. 2. Nathan Said：

There are 900 three digit numbers. The first one-hundred have a one in them, for the other sets of one-hundred, each has 19 of that set containing a 1 digit. 8*19 is 152, add 100 and divide by 900, e.g. 252/900 is 28%

3. 3. Chris Said：

Hi Karl, you got your question right.

The rest is as Nathan said.

So what is the probabilty that a number between 100 and 999 (inclusive) contains two 1’s, given that it contains at least one 1?

4. 4. Nathan Said：

Of the 900 numbers, 252 contain at least one one as shown above. of those, 27 have at least two more more one’s. This give a 3/28 or 10.7% chance that a number has at least two ones, given that you know it contains at least one one.

5. 5. Gish Said：

13/45 or 260 in 900

6. 6. Shannon Said：

I got 280 of 900 or 14/45

7. 7. Karl Sharman Said：

Chris – Post 3 – I think that there is a probability of…

252 with 1 number 1
27 with 2 number 1’s

For any 3 digit number there are 252 possible and equally likely combinations where at least 1 number is a 1.
Only 27 of those combinations has 2 number ones in it.

So…. deep breath…. 1 in 9.333?

8. 8. Subodh Arora Said：

9. 9. todd Said：

well there are 900 3 digit numbers and there are.. 1 10 10 + 8 1 1 + 8 10 1 + 8 1 10 + 1 = 269 with the number one in at least one spot. I am 9% sure that that is right.. i am in math 12 and we are working on probabilities right now. im going to ask the teacher tomorrow though

10. 10. todd Said：

oh i am wrong. i realized that i double counted a few things.. i get 252 now

11. 11. Dual Aspect Said：

Hi Karl,

Could you update the “Adds Up To a Thousand” puzzle with a solution please?

Nathan, Wiz and I all have different answers for the number of unique triplet combinations and it’s been a few days with no new posts (I think Chris’s “Girls Girls Girls” post has had all the attention lately).

Cheers.

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