Question

There are three levels (levels 1 – 3) of assessment that a student must pass to complete an external course. From previous information, out of 1,000 students who undertook the course, the failures were 150 at level 1; 300 at level 2; and 120 at level 3. To be awarded a degree, students’ needs to pass all three levels. To be awarded a diploma, a student must pass at least 2 levels. Students who can pass only 1 level gets a certificate.

if they want to get the number of students that can get a certificate to 500, what should be the total intake for the course.    

	A.	1300
	B.	1122
	C.	1390
	D.	2527
	E.	500

Answer 1

Given data:

Fail at level 1 is 150 out of 1000

means Probability for fail level 1 P(1) =150/1000 = 0.15

fail at level 2 is 300 out of 1000

means Probability for fail level 2 P(2) =300/1000 = 0.3

fail at level 3 is 120 out of 1000

means Probability for fail level 3 P(3) =120/1000 = 0.12

for getting degree they should pass all 3 level

for getting deploma they should pass atleast 2 levels

for getting certificate they should pass 1 level

probability for passing 1 level = pass level 1 & fail Level 2 &3 or pass level 2 & fail Level 3 & 1 or pass level 3 & fail Level 1 & 2

it means .,

P(pass 1 level) = (1-P(1))*P(2)*P(3)+(1-P(2))*P(3)*P(1)+(1-P(3))*P(1)*P(2)

=0.85*(0.3)*(0.12)+0.7*(0.12)*(0.15)+0.88*(0.15)(0.3)

= 0.0828

number of students that can get a certificate = 500 = number of total intake * P(pass 1 level)

500 = number of total intake * 0.0828

number of total intake =500/0.0828

=6039 students.

But in case above failure rate may be  pass rate the solution will be:

pass at level 1 is 150 out of 1000

means Probability for pass level 1 P(1) =150/1000 = 0.15

pass at level 2 is 300 out of 1000

means Probability for pass level 2 P(2) =300/1000 = 0.3

pass at level 3 is 120 out of 1000

means Probability for pass level 3 P(3) =120/1000 = 0.12

for getting degree they should pass all 3 level

for getting deploma they should pass atleast 2 levels

for getting certificate they should pass 1 level

probability for passing 1 level = pass level 1 & fail Level 2 &3 or pass level 2 & fail Level 3 & 1 or pass level 3 & fail Level 1 & 2

it means .,

P(pass 1 level) = (P(1))*(1-P(2))*(1-P(3))+(P(2))*(1-P(3))*(1-P(1))+(P(3))*(1-P(1))*(1-P(2))

=0.15*(0.7)*(0.88)+0.3*(0.88)*(0.85)+0.12*(0.85)(0.7)

= 0.3882

number of students that can get a certificate = 500 = number of total intake * P(pass 1 level)

500 = number of total intake * 0.3882

number of total intake =500/0.3882

=1289 students. approx. 1300 students

OPTION- A

NB: Dear, kindly check the question if they gave passing rate. option A is the aswer. else it get a 6039 intake. kindly recheck and comment it. i am here for help you more.,