Bag B_1 contains 6 white and 4 blue balls, Bag B_2 contains 4 white and 6 blue balls, and Bag B_3 contains 5 white and 5 blue balls. One of the bags…

Bag $\displaystyle \mathrm{B}_1$ contains $\displaystyle 6$ white and $\displaystyle 4$ blue balls, Bag $\displaystyle \mathrm{B}_2$ contains $\displaystyle 4$ white and $\displaystyle 6$ blue balls, and Bag $\displaystyle \mathrm{B}_3$ contains $\displaystyle 5$ white and $\displaystyle 5$ blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag $\displaystyle \mathrm{B}_2$, is :