Use the counting principle to find the probability of choosing the 8 winning lottery numbers when the numbers are chosen at random from 0-9
The probability of choosing the 8 winning lottery numbers when the numbers are chosen at random from 0-9 is:
\(\dfrac{1}{10^8}\)
We know that there are total 10 numbers from 0-9
As all of the 8 numbers may repeat.
Hence, total number of ticket number possible are:10×10×10×10×10×10×10×10=10^8
Now the probability of choosing the 8 winning lottery numbers is given by:
\(Probability=\dfrac{1}{10}\times \dfrac{1}{10}\times \dfrac{1}{10}\times \dfrac{1}{10}\times \dfrac{1}{10}\times \dfrac{1}{10}\times \dfrac{1}{10}\times \dfrac{1}{10}=\dfrac{1}{10^8}\)
Hence, the answer is:
\(\dfrac{1}{10^8}\)