To find the probability, we need to determine the number of favorable outcomes (numbers that satisfy the given condition) and the total number of possible outcomes (all four-digit numbers where the first digit is nonzero).
First, let's identify the possible values for each place value:
- Thousands place: It can take any value from 1 to 9.
- Hundreds place: Since it must be greater than the thousands place, it can take any value from 2 to 9.
- Tens place: It must be greater than the hundreds place, so it can take any value from 3 to 9.
- Ones place: It must be greater than the tens place, so it can take any value from 4 to 9.
Now, let's find the favorable outcomes. We need to find the number of four-digit numbers that satisfy the given conditions.
For the thousands place, there are 9 possible values (1 to 9).
For the hundreds place, there are 7 possible values (from 2 to 9, excluding the value chosen for the thousands place).
For the tens place, there are 5 possible values (from 3 to 9, excluding the values chosen for the thousands and hundreds places).
For the ones place, there are 4 possible values (from 4 to 9, excluding the values chosen for the thousands, hundreds, and tens places).
To calculate the total number of favorable outcomes, we multiply the number of possibilities for each place: 9 x 7 x 5 x 4 = 1,260.
Now, let's find the total number of possible four-digit numbers where the first digit is nonzero.
The thousands place can have 9 possible values (from 1 to 9).
The hundreds place can have 9 possible values (from 0 to 9, excluding the value chosen for the thousands place).
The tens place can have 9 possible values (from 0 to 9, excluding the values chosen for the thousands and hundreds places).
The ones place can have 9 possible values (from 0 to 9, excluding the values chosen for the thousands, hundreds, and tens places).
To calculate the total number of possible outcomes, we multiply the number of possibilities for each place: 9 x 9 x 9 x 9 = 6,561.
Therefore, the probability of selecting a four-digit number that satisfies the given conditions is 1,260/6,561 = 0.192 or 19.2%.
So, the probability is approximately 0.192 or 19.2%.