For entry to a science college, students must first sit a written test and then take a practical test. Each student may have at most two tries at the written test. A second try is permitted only if the first try is unsuccessful. No student may attempt the practical test more than once. If both written-test attempts are failed, the practical test cannot be taken. The chance that a student passes the written test on the first attempt is $0.8$. If the first written-test attempt is failed, the chance of passing on the second attempt is $0.6$. The chance that a student passes the practical test is always $0.3$.
(a)[3]
Draw a tree diagram to model this information, and show the probabilities on the branches.
(b)[2]
Find the probability that a randomly chosen student will succeed in gaining a place at the college.
(c)[2]
Find the probability that a randomly chosen student passes the written test at the first attempt, given that the student succeeds in gaining a place at the college.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A completely correct labelled tree diagram” …