A student travels to college by either of two routes, A or B. The probability that they use route A is 0.3, and the probability that they are passed by a bus on their way to college on any particular day is 0.034.

They are twice as likely to be passed by a bus when they use route B as when they use route A.

a. Use the tree diagram opposite to form and solve a pair of simultaneous equations in x and y.

b. Find the probability that the student uses route B, given that they are not passed by a bus on their way to college.