The probability that the numbers on both balls are odd numbers is 
<em><u>Solution:</u></em>
<em><u>The probability of an event is given as:</u></em>

Given that, bowl contains 25 balls numbered 1 to 25
The sample space is given as;
{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 }
Therefore,
Total number of possible outcomes = 25
A ball is drawn and its number is noted. Without replacing the first ball, another ball is drawn.
Numbers on both balls are odd numbers
<em><u>Let us first find the probability that first ball is odd</u></em>
Favorable outcome = odd numbers
Favorable outcome = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25
Number of favorable outcomes = 13
Thus, probability is given as:

Now Without replacing the first ball, another ball is drawn.
<em><u>Find the probability that second ball is odd number</u></em>
Without replacing means that ball is not put back into bowl
So, sample space = 25 - 1 = 24
Total number of possible outcomes = 25
Number of favorable outcomes = 13 - 1 = 12
Thus, probability is given as:

<em><u>Probability that the numbers on both balls are odd numbers is:</u></em>
Multiply both the probabilities

Thus, probability that the numbers on both balls are odd numbers is 