Drivers who wish to obtain an advanced driving qualification must pass a theory test and a skills test.

Drivers must pass the theory test first and are allowed up to two attempts. The probability of passing the theory test on the first attempt is 0.7, and the probability of passing on the second attempt is 0.6.

Drivers who pass the theory test are then allowed up to three attempts to pass the skills test. The probability of passing the skills test on any attempt is 0.2.

(a) Complete the tree diagram to illustrate this information, showing all the probabilities. [2]

(b) Show that the probability that a randomly chosen driver passes the theory test at the first attempt and the skills test at the second attempt is 0.112. [1]

(c) Find the probability that a randomly chosen driver obtains the advanced driving qualification. [3]

(d) Find the probability that a randomly chosen driver passes the theory test at the first attempt given that the driver obtained the qualification. [3]