The integers from 1 to 25 include both odd and even numbers. The odd integers within this range are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, and 25.
To count the odd numbers:
- The sequence of odd numbers can be represented as 1, 3, 5, ..., 25.
- This sequence is an arithmetic series where the first term (a) is 1, the common difference (d) is 2, and the last term (l) is 25.
To find the number of terms in this sequence (n), we can use the formula for the nth term of an arithmetic sequence: \[ l = a + (n-1)d \] \[ 25 = 1 + (n-1) \cdot 2 \] \[ 25 - 1 = (n - 1) \cdot 2 \] \[ 24 = (n - 1) \cdot 2 \] \[ 12 = n - 1 \] \[ n = 13 \]
Thus, there are 13 odd numbers between 1 and 25. So the number of favorable outcomes for choosing a card with an odd number is 13.