Question

find the probability of getting any five - digit number where all the digits are the same in a lottery game that consists of selecting a five - digit number. (express your answer as a decimal; do not round.)
the probability of getting any five - digit number where all the digits are the same is

Explanation:

Step1: Determine the total number of five - digit numbers

The smallest five - digit number is \(10000\) and the largest is \(99999\). The total number of five - digit numbers is \(9\times10\times10\times10\times10=90000\) (the first digit can be any digit from \(1 - 9\), and the other four digits can be any digit from \(0 - 9\)).

Step2: Determine the number of five - digit numbers with all digits the same

There are \(9\) such numbers: \(11111,22222,\cdots,99999\)

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{9}{90000}\)

Step4: Simplify the fraction

\(\frac{9}{90000}=\frac{1}{10000}=0.0001\)

Answer:

\(0.0001\)