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# math question counting

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Sam writes down the integers 1-999 inclusive. Sam chooses one of the digits written down at random. What is the probability that Sam chooses a 7?

Jun 30, 2023

#1
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There are a total of 900 integers from 1 to 999 inclusive. The digit 7 can appear in the hundreds, tens, or units place. In the hundreds place, there are 100 numbers that have a 7. In the tens place, there are 90 numbers that have a 7. And in the units place, there are 90 numbers that have a 7. So, there are a total of 100 + 90 + 90 = 280 numbers that have a 7.

Therefore, the probability that Sam chooses a 7 is 280 / 900 = 14/45.

Jun 30, 2023
#3
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Thanks, that's right!

Guest Jul 7, 2023
#2
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First, you have to count all the digits between 1 and 999.

1 to 9 ==9 digits

10 to 99 ==90 x 2 ==180 digits

100 to 999 ==900 x 3 ==2,700 digits

Total =9 + 180 + 2700 ==2,889 digits between 1 and 999

There are: 300 "sevens" between 1 and 999.

Therefore, the probability of picking a "7" is:

300 / 2,889 ==100 / 963

Jun 30, 2023