Final answer:
The probability that both balls drawn from a bowl of 25 balls (numbered 1 to 25) are odd is 13/50. This is calculated by taking the probability of drawing an odd ball on the first draw (13/25) and multiplying it by the probability of drawing an odd ball on the second draw (12/24 or 1/2) after the first ball is not replaced.
Step-by-step explanation:
We are looking to find the probability that both balls drawn from the bowl are odd numbers. Since there are 25 balls, with numbers from 1 to 25, there are 13 odd-numbered balls (since every other number is odd starting from 1).
When the first ball is drawn, the probability that it is odd is 13 out of 25 (13/25). Without replacing the first ball, now only 24 balls remain, out of which 12 are odd (since we removed one odd ball). Therefore, the probability that the second ball is odd is 12 out of 24 (12/24), which simplifies to 1/2.
To find the combined probability of both events, we multiply the probabilities together:
P(first ball odd AND second ball odd) = P(first ball odd) × P(second ball odd) = (13/25) × (1/2) = 13/50.
Therefore, the probability that both balls are odd numbers is 13/50.