Applicants to Drydale College sit an entrance examination. For any student, the possible outcomes are accepted, rejected, or told to sit a further test, with probabilities $0.3$, $0.2$ and $0.5$ respectively. If a second test is taken, the outcomes and probabilities are exactly the same as for the first test. A student who must sit a third test is accepted with probability $0.25$ and rejected with probability $0.75$.
(a)[2]
Construct a tree diagram to represent this information, and include all of the probabilities.
(b)[2]
Work out the probability that a student chosen at random from those applying to Drydale College is accepted.
(c)[3]
Work out the probability that a randomly chosen applicant to Drydale College takes at least two tests, given that the student is accepted.
(d)[2]
Three friends apply to Drydale College. Find the probability that all three are rejected.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Completely correct tree diagram with all labels shown.” …