Question

A bowl contains 25 balls numbered 1 to 25. A ball is drawn and its number is noted. Without replacing the first ball, another ball is drawn.
The probability that the numbers on both balls are odd numbers is .

Answer 1

Let A = the event that the first ball is odd number
and B = the event that the second ball is odd number

In the beginning, there are 25 balls which contain 13 balls of odd numbers. So the probability for the first selection (as to expect you would draw a ball of an odd number) is
P(A) = 13/25

After the selection, the rule does not allow replacement. So, there are 24 balls left containing now 12 balls of odd numbers. So the probability for the second selection (as to expect you would draw also a ball of odd number) is
P(B) = 12/24 = 1/2

Multiplying the two probabilities obtains
P(2 odd numbers) = 13/25 * 1/2 = 13/50