At the end of a training programme, students have to pass an exam to gain a cirtificate.

The probability of passing the exam at the first attempt is 0.75

Those who fail are allowed to re-sit.

The probability of passing the re-sit is 0.6

No further attempts are allowed.

(a)(i) Create a tree diagram.

(ii)What is the probability that a student fails to gain a certificate?

(b) Three students take the exam.

What is the probability that all of them gain a certificate?

Guest Nov 10, 2014

#1**+5 **

a) A tree diagram is hard to explain in words, but I'm not sufficiently computer literate to provide a drawing.

So: let the diagram start at point A.

From A, there are two paths, one is a successful path to B (with value 0.75) and the other is an unsuccessful path to C (with value 0.25).

There is no path from B because there is no need to take another test.

From point C, there are two paths, one is a successful path to D (with value 0.60) and the other is an unsuccessful path to E (with value 0.40)

There are no paths from D or E.

b) The only way for a student to fail is to go from A to C (0.25) and from C to E (0.40). To find the probability for going from A to E is 0.25 x 0.40 = 0.10.

c) Since the protability of failing is 0.10, the probability of succeeding is 0.90.

The probability of all succeeding is 0.90 x 0.90 x 0.90 = 0.729.

geno3141
Nov 12, 2014