# SOLUTION: suppose you select a 3 digit number at random from the set of all positive 3 digit nimbers . find each probability or odds 1) odds in favor of a multiple of 10 2) odds agai

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 Click here to see ALL problems on Probability-and-statistics Question 517284: suppose you select a 3 digit number at random from the set of all positive 3 digit nimbers . find each probability or odds 1) odds in favor of a multiple of 10 2) odds against 243 or 244 3) odds against a number greater than 400Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!suppose you select a 3 digit number at random from the set of all positive 3 digit nimbers. ```First we need to determine the number of 3 digit numbers. The largest 3 digit number is 999. Among the first 999 counting numbers, the first 99 of them have less that 3 digits, so the number of 3 digit counting numbers is 999-99 or 900. ``` 1) odds in favor of a multiple of 10 ```Now we have to find the number of 3-digit numbers which are multiplse of 10. They are 100, 110, 120, ... 990. They are all the 2-digit numbers 10, 11, 12, ... 99 with a zero added on the end. So we only need to find the number of two digit numbers. Among the first 99 counting numbers, the first 9 of them have less that 2 digits, so the number of 2 digit counting numbers is 99-9 or 90. And that's the same as the number of 3-digit multiples of 10. So out of the 900 3-digit numbers, 90 of them are multiples of 10. The other 900-90 or 810 are not multiples of 10. So the odds in favor of a multiple of 10 is 90:810 which reduces to 1:9 ``` 2) odds against 243 or 244 ```Out of the 900 3-digit numbers, 2 of them are 243 or 244, and the other 900-2 or 898 are neither of those, so the odds against those two are 898:2 which reduces to 449:1 ``` 3) odds against a number greater than 400. ```Among the first 999 counting numbers, the first 400 of them are not greater than 400, and the other 999-400 or 599 counting number are 3-digit numbers greater than 400. The other 900-599 or 301 3-digit numbers are not greater than 400. So the odds against a number greater than 400 are 301:599 Edwin```