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    Here's how I approached to the solution

    We can take 1 ball from Bag1 and 2 from Bag2

    Probability of 2 black and 1 red

    From Bag1 either we get the red or black ball From Bag2 either we get both ball black or one red and one black. (Incase, if Bag1 got a black ball)

    1st Possibility

    Bag1: 4/9 (Red Ball) Bag2:7/10 (1st Black Ball taken out) -> 6/9 (2nd Black Ball)

    2nd Possibility

    Bag1: 5/9 (Black Ball) Bag2: 7/10 (1st Black Ball) -> 3/9 (2nd Red Ball)

    3rd Possibility

    Bag1: 5/9 (Black Ball) Bag2: 3/10 (1st Red Ball ) -> 7/9 (2nd Black Ball)

    Multiplying and combining all possibility Possibility#1 + Possibility#2 + Possibility#3 = 7/15