CAT 2023 Probability — Previous Year Question

To select a group out of three, an unbiased die is rolled. If the dice shows 1, then group X is chosen. If it shows 2 or 3, then group Y is chosen and if it shows 4, 5 or 6, then group Z is chosen, Group X has 3 girls, 2 boys. Group Y has 3 girls and 4 boys. Group Z has 4 girls and 5 boys. The dice is rolled and the group is chosen, if it is known that girl is chosen, then find probability that she is chosen from group Y?