Solution. We begin by drawing part of the tree diagram

We begin by drawing part of the tree diagram. Because we do not know how many times she kicks the ball, the diagram potentially has an infinite number of branches.

a) From the tree diagram we can see that the only branch of the tree where she never hits the net is the one marked *.

Thus

Taking logs of both sides

Using the laws of logs

The inequality changes because log 0.3 is negative.

since

b) In this case the branch of the tree diagram that we are interested in is again the one marked *.

We want