Question

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 $7$?

Answer 1

100/963

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