JEE Advanced 2019 Mathematics question

There are three bags , and . The bag contains 5 red and 5 green balls, contains 3 red and 5 green balls, and contains 5 red and 3 green balls. Bags , and have probabilities , and respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

• (A)Probability that the chosen ball is green, given that the selected bag is , equals Correct
• (B)Probability that the chosen ball is green equals Correct
• (C)Probability that the selected bag is , given that the chosen ball is green, equals
• (D)Probability that the selected bag is and the chosen ball is green equals