+0  
 
0
333
2
avatar

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

Best Answer 

 #2
avatar+26412 
+5

Here's a tree diagram:

Tree diagram

 

.

Alan  Nov 12, 2014
Sort: 

2+0 Answers

 #1
avatar+17711 
+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
 #2
avatar+26412 
+5
Best Answer

Here's a tree diagram:

Tree diagram

 

.

Alan  Nov 12, 2014

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details