# How do you use the Counting Principle to find the probability of choosing the 5 winning lottery numbers when the numbers are chosen at random from 0 to 9?

How do you use the Counting Principle to find the probability of choosing the 5 winning lottery numbers when the numbers are chosen at random from 0 to 9?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Kash Osborn
We have a 5-digit number and we're trying to calculate the odds of guessing the number correctly.
For each digit, there is a 1/10 chance of getting it right. There are 5 digits, and so according to the Counting Principle, we multiply all of them together:
$\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)=\frac{1}{{10}^{5}}=\frac{1}{10,000}=0.0001$