Here's the proof, if you want to list out all the possible outcomes.

The 25 possible outcomes of picking a random number from each set will be: (A, B)
1 11, 1 22, 1 33, 1 44, 1 55,
2 11, 2 22, 2 33, 2 44, 2 55,
3 11, 3 22, 3 33, 3 44, 3 55,
4 11, 4 22, 4 33, 4 44, 4 55,
5 11, 5 22, 5 33, 5 44, 5 55.

Out of these 25 outcomes, only 9 of them have both numbers that are odd:
1 11, 1 33, 1 55,
3 11, 3 33, 3 55,
5 11, 5 33, 5 55.

Hence probability of getting odd in A and B is 9/25.



A better explanation of the answer in the picture is:
Probability of getting odd in A is 3/5
Probability of getting odd in B is 3/5

In school, they teach if you want an outcome of something AND something, you multiply.

Hence, Probability of getting odd in A AND B is 3/5 × 3/5 which is 9/25.