May 2019 Q6
a) Define the following terms in probability theory:
i) Collectively exhaustive events. (2 marks)
View Solution
A set of events is jointly or collectively exhaustive if at least one of the events must occur.
ii) The complement of an event. (2 marks)
View Solution
The complement of an event is the event not occurring. Thus, the complement of Event A is Event A not occurring. (The probability that Event A will not occur is denoted by P(A’)).
b) A survey of The Institute of Chartered Accountants (Ghana) students asked the question ‘What is your favourite sport?’ The results are summarised below:
Required:
i) What is the probability of selecting a student whose favourite sport is boxing? (2 marks)
View Solution
There are 171 students who chose boxing as their favourite sport and a total of 545 students levelicipated in the survey
P(Boxing fan) =171/545
ii) What is the probability of selecting a Level 1 student? (2 marks)
View Solution
A total of 155 students are in Level 1
P(selecting Level 1 student)= 155/545=31/109 or 0.284
iii) If the student selected is a Level 2 student, what is the probability that the student prefers hockey? (3 marks)
View Solution
70 students prefer hockey and a total of 210 students are in Level 2
P(Hockey fan/Level2 student)=70/210=1/3 or 0.333
iv) If the student selected is a Level 2 student, what is the probability that the student prefers football or hockey? (3 marks)
View Solution
A total of (84+70) 154 students prefer football or hockey
P(Football or Hockey fan/Level 2 student) = 154/210=11/15 or 0.733
v) If the student selected prefers football, what is the probability that the student is a Level 1 student? (3 marks)
View Solution
A total of 211 students prefer football and 68 of them are in Level 1
P(Level 1 student/Football fan)=68/211 or 0.322
vi) If the student selected is a Level 3 student, what is the probability that the student prefers football, boxing or hockey? (3 marks)
View Solution
A total of 180 students are in Level 3 and (74+47+59) 121 of them prefer football, boxing or hockey
P(Football, Boxing or hockey fan/Level 3)=180/180 or 1