Answer to Question #311614 in Statistics and Probability for isaac

Question

A university has analyzed the results of 1,000 students after the first year examinations. The result of the analysis is summarized below

 

Types of sponsorship

Examination results

Government

Private

Church

Students who were to be discontinued

155

150

105

Students who passed the examination

180

195

170

Students who were to sit for a supplementary paper

20

5

20

Required

The probability that a student was discontinued or was required to sit for a supplementary paper                                                                                                           

The probability that a student was a government sponsored           

The probability that a privately sponsored student passed the examination     

The probability that a student was church sponsored and was required to sit for a supplementary paper                                              

Answer 1

Total number of students $=1000$

(a) Probability that a student was discontinued or required to sit for a supplementary.

Let D be students that were discontinued and S those that sat for supplementary.

$P(D \cup S) = P(D)+P(S)$

$P(D \cup S) =P(D)+P(S)$

$=\dfrac{410}{1000}+\dfrac{45}{1000}=0.455$

(b) The probability that a student was a government sponsored

Let G represent students that were government sponsored.

$P(G) =\dfrac{155+180+20}{1000}$

$P(G)=0.355$

(c) The probability that a privately sponsored student passed the examination

Let PS represents privately sponsored students who passed the exam.

$P(PS)=\dfrac{195}{1000}=0.195$

(d) The probability that a student was church sponsored and was required to sit for a supplementary

Let CS represent the church sponsored students who sat for supplementary

$P(CS)=\dfrac{20}{1000}=0.02$