There are three bags $\mathrm{B}_1, \mathrm{~B}_2$ and $\mathrm{B}_3$. The bag $\mathrm{B}_1$ contains 5 red and 5 green balls, $\mathrm{B}_2$ contains 3 red and 5 green balls, and $\mathrm{B}_3$ contains 5 red and 3 green balls, Bags $\mathrm{B}_1, \mathrm{~B}_2$ and $\mathrm{B}_3$ have probabilities $\frac{3}{10} \cdot \frac{3}{10}$ 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 ?
Select ALL correct options:
A
Probability that the selected bag is $B_3$ and the chosen ball is green equals $\frac{3}{10}$
B
Probability that the chosen ball is green equals $\frac{39}{80}$
C
Probability that the chosen ball is green, given that the selected bag is $\mathrm{B}_3$ equals ${ }_8^3-$
D
Probability that the selected bag is $\underbrace{\mathrm{B}_4}_3$, given that the chosen balls is green, equals $\frac{5}{13}$
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