Answer to Question #308984 in Statistics and Probability for joy

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                                                                         (1mark)

The probability that a student was a government sponsored           (1mark)

The probability that a privately sponsored student passed the examination                                                                                                           (2marks)

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

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

$=0.455$

(b) Probability that a student was government sponsored.

Let G be the students sponsored by government.

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

P(G) $= 0.355$

(c) Probability that private student passed the exam .

Let pp be the private students that passed the exams.

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