There are three bags $B _ { 1 } , B _ { 2 }$ and $B _ { 3 }$. The bag $B _ { 1 }$ contains 5 red and 5 green balls, $B _ { 2 }$ contains 3 red and 5 green balls, and $B _ { 3 }$ contains 5 red and 3 green balls. Bags $B _ { 1 } , B _ { 2 }$ and $B _ { 3 }$ have probabilities $\frac { 3 } { 10 } , \frac { 3 } { 10 }$ and $\frac { 4 } { 10 }$ 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 $B _ { 3 }$, equals $\frac { 3 } { 8 }$ (B) Probability that the chosen ball is green equals $\frac { 39 } { 80 }$ (C) Probability that the selected bag is $B _ { 3 }$, given that the chosen ball is green, equals $\frac { 5 } { 13 }$ (D) Probability that the selected bag is $B _ { 3 }$ and the chosen ball is green equals $\frac { 3 } { 10 }$
There are three bags $B _ { 1 } , B _ { 2 }$ and $B _ { 3 }$. The bag $B _ { 1 }$ contains 5 red and 5 green balls, $B _ { 2 }$ contains 3 red and 5 green balls, and $B _ { 3 }$ contains 5 red and 3 green balls. Bags $B _ { 1 } , B _ { 2 }$ and $B _ { 3 }$ have probabilities $\frac { 3 } { 10 } , \frac { 3 } { 10 }$ and $\frac { 4 } { 10 }$ 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 $B _ { 3 }$, equals $\frac { 3 } { 8 }$\\
(B) Probability that the chosen ball is green equals $\frac { 39 } { 80 }$\\
(C) Probability that the selected bag is $B _ { 3 }$, given that the chosen ball is green, equals $\frac { 5 } { 13 }$\\
(D) Probability that the selected bag is $B _ { 3 }$ and the chosen ball is green equals $\frac { 3 } { 10 }$