Suppose you drew a white ball. Both first Urn (A), and the second Urn (B), have a white balls in them (2 and 5 resp.). The choice whether we will draw a ball from Urn A or Urn B depends on whether the coin showed heads or tails.
The question asks you to tell the probability of coin showing a head if a white ball had been drawn. Alternatively, it asks you to tell the probability of the ball being from Urn A (since we chose A if we get head), if it is a white ball.
Let us define W to be the event of ball being white. A of ball being from urn A, and B of ball being from Urn B.
P(A|W) (Our answer) = P(A.W)/P(W)
Now, *P(A.W) = 2/9, P(B.W) = 5/11, P(W) = 1/2*P(A.W) + 1/2*P(A.B)*
Plug the value. Get the answer. As to your question, the relationship between tossing a coin and selecting a ball is that outcome of the coin decides which urn we are going to draw from, and thus changes the probability distribution of drawing the ball, or chances of getting a white(or a black ball).