One day, River writes down the numbers $1,$ $2,$ $/dots,$ $999.$ River chooses one of the digits written down at random. What is the probability that River chooses a $7$?

100/963

Step-by-step explanation:

The number 1,2,3, ...,999 is written down.

First, we determine the total number of digits written down

1-9 = 9 digits 10-99 = 2 (99 - 10 + 1) = 2 (90) digits 100-999=3 (999 - 100 + 1) = 3 (900) digits

Total Number of digits=9+2 (90) + 3 (900) = 2889

Number of Digit 7 between 1 and 999

In the Units' place, 7 occurs once every decade (7, 017 ... 997) = 10 X 10 = 100 times In the Tens place, 7 occurs in the ten times every century (70-79, 170-179, ..., 970-979) = 10 X 10 = 100 times In the hundreds' place, 7 occurs once in the hundreds' place (700, 701, ..., 799) = 100 times

Therefore, the number 7 will be found a total of 300 times between 1 and 999.

Therefore, the probability of selecting a "7" = 300/2889

= 100/963