Page 13 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
23. A company manager has to visit four of the ten subsidiaries that the company owns.
(a) In how many different ways can the manager plan his itinerary in visiting four of the twelve
subsidiaries?
(b) How many sets of four companies are there from which the manager can pick one set to visit?
24. A company has 10 construction workers. The manager plans to assign 3 to job site A, 4 to job site B,
and 5 to job site C. In how many different ways can the manager make this assignment?

2.2 Probability
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Sample spaces 2
The scientists perform experiments to produce observations or measurements that will assist them in arriving
at conclusions. In statistics the word experiment is used to describe any process that generates raw data or
outcome. Thus, an outcome is a result of some activity. For example:
Rolling a die has six outcomes: 1, 2, 3, 4, 5, 6
A sample space is a set of all possible outcomes for an activity and is represented by S. For example: The
sample space for rolling a die is: S = {1, 2, 3, 4, 5, 6}

The sample space for tossing a coin consists of the two outcomes, head H and tail T is: S = {H, T}
An event is the collection of outcomes of particular interest in an experiment. For the experiment of tossing
a coin, suppose we are interested only in getting a head, then this event consists of a single element, H.
Thus, in this example of tossing a coin;
The event that a head occurs is: E = {H},
If a coin is tossed 3 times in succession;
The event that the number of heads is appears more than once is: E = {HHH, HTH, THH, HHT},

Obviously the event E is the subset of the sample space S.
For another example in rolling a die;
The event of obtaining a 3 is: E = {3},
The event of obtaining an odd number is: E = {1, 3, 5}

Example 12

Consider the experiment of a team’s result in a football match. Determine the sample space, S.

Solution: The possible outcome of the team’s result in a football match is win, lose or draw.
So, the sample space is S = {win, lose, draw}.

Example 13

For the experiment in Example 12, write the following events.
(a) Event A: The team wins the match
(b) Event B: The team does not lose the match

Solution: (a) Event A has only one possible outcome, win, so the event A is: A = {win}
(b) Two outcomes fulfil this given condition: win or draw. So the event B is:
B = {win, draw}

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