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

Sample space {1,2,3,..........,25} = 25 Total outcomes
Sample space  odd numbers{1,3,5,7,9,11,13,15,17,19,2,23,25} = 13 favorable outcomes.

P(drawing one even number) = 13/25

There is no replacement, then the number of favorable outcome
becomes 12 (since one ball already drawn) and the total outcome
becomes 24 instead of 25.

P(drawing a second odd number) = 12/24 = 1/2

P( drawing one odd AND another odd) = (13/25).(1/2) =13/50 = 0.26

Answer 2

25 balls, 13 are odd

first pick = 13/25 probability of picking an odd

2nd pick = 12/24 = 1/2 probability

13/25 x 1/2 = 13/50 probability