JEE Advanced 2024 — Paper 2 — Question 9

A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i=1,2,3$, let $W_{i}, G_{i}$, and $B_{i}$ denote the events that the ball drawn in the $\mathrm{i}^{\text {th }}$ draw is a white ball, green ball, and blue ball, respectively. If the probability $P\left(W_{1} \cap G_{2} \cap B_{3}\right)=\frac{2}{5 N}$ and the conditional probability $P\left(B_{3} \mid W_{1} \cap G_{2}\right)=\frac{2}{9}$, then $N$ equals $\qquad$