Subsection 3.2.1 Introduction to Probability
Teacher Resource 3.2.2.
To assist your teaching, we have prepared lesson resources, aligned with this textbook and the CBC. The Lesson Plan links to syllabus learning outcomes and provides suggest time allocations. The Step-by-Step Guide provides more detailed guidance on how to teach the content, including suggested questions to ask learners, and possible answers.
Learner Experience 3.2.1.
\({\color{black} \textbf{Work in groups}}\)
Write down 3 events that could happen today (e.g., “It will rain” or “I will be late to school”)
Predict the probability of each event: \(\textbf{Is it likely, unlikely, or certain}\text{?}\)
\({\color{black} \textbf{Key Takeaway}}\)
\(\text{Probability}\) is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where:
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\(0\) means the event is impossible.
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\(1\) means the event is certain.
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A probability closer to \(1\) indicates a higher likelihood of the event occurring.
Probability is always between 0 and 1
\(\text{Probability Scale}\)
\({\color{black} \text{Key Terms in Probability}}\)
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\(\text{Experiment}\) - A process that leads to a specific result.
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\(\text{Outcome}\) - A possible result of an experiment.
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\(\text{Event}\) - A collection of one or more outcomes.
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\(\text{Sample Space (S)}\) - The set of all possible outcomes.
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\(\text{Probability (P)}\) - A measure of how likely an event is to occur.
Probability is widely used in everyday life, including:
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\(\text{Weather Forecasting}\) - Meteorologists predict the likelihood of rain based on past data.
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\(\text{Sports}\) - Coaches analyze the probability of winning based on past performance.
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\(\text{Medicine}\) - Doctors assess the probability of a patient responding to treatment.
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\(\text{Finance and Insurance}\) - Insurance companies use probability to determine policy pricing.
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\(\text{Games of Chance}\) - Dice rolling and card games use probability.
Learner Experience 3.2.2.
\({\color{black} \textbf{Work in groups}}\)
Kanyama rolls a fair six-sided die. What is the probability of Kanyama rolling a \(4\)
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Identify the Sample Space.
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Identify the Favorable Outcomes
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Apply the Probability Formula
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Discuss and compare answers
\({\color{black} \textbf{Key Takeaway}}\)
A simple event is an event that consists of only one outcome in the sample space.
The probability of a simple event is given using the formula
\begin{gather*}
\textbf{P(E)} = \frac{\textbf{Number of favorable outcomes}}{\textbf{Number of Outcomes}}
\end{gather*}
where;
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Favorable outcomes refer to the specific event we are interested in
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Total outcomes refer to all possible outcomes in the sample space
Example 3.2.3.
A bag contains 5 red balls and 3 blue balls. If one ball is picked at random, what is the probability that it is red?
Solution.
Total number of balls \(\textbf{ = 5 + 3 = 8}\)
Number of red balls \(\textbf{ = 5}\)
Given a bag with \(5\) red balls and \(3\) blue balls, the possible outcomes when picking one ball are
\(\textbf{S = {Red,Blue}}\)
Total outcomes \(\textbf{ = 5 + 3 = 8}\)
Probability of drawing a red ball is given by:
\(\textbf{P(Red)}=\frac{\textbf{Number of favorable outcomes}}{\textbf{Number of Outcomes}} = \frac{5}{8}=\textbf{0.625}\)
Example 3.2.4.
A teacher at Sironga Secondary school randomly selects a student from a class of 30 students. If there are 12 girls and 18 boys in the class, what is the probability that the selected student is a girl?
Solution.
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The number of favorable outcomes that is choosing a girl = \(\textbf{12}\)
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Now, Applying our formula gives\begin{gather*} \textbf{P(Girl)}=\frac{\textbf{Number of girls}}{\textbf{Total number of students}} \end{gather*}\begin{gather*} = \frac{12}{30} \end{gather*}\begin{gather*} =\textbf{0.4} \end{gather*}
Checkpoint 3.2.5.
Checkpoint 3.2.6.
Checkpoint 3.2.7.
Checkpoint 3.2.8.
Exercises Exercises
1.
What is the probability of selecting the letter ’a’ from the name "Mukabwa"?
2.
A deck of standard playing cards has 52 cards. What is the probability of drawing the 5 of Hearts?
3.
A bag has 3 yellow marbles, 5 black marbles, and 2 white marbles. What is the probability of selecting a white marble?
4.
A month is selected at random from a year. What is the probability that it is June?
5.
A coin is tossed. What is the probability of getting tails?
6.
A box contains tickets numbered from 1 to 10. What is the probability of drawing a ticket with the number 7?
7.
A class has 25 students, and one student is chosen at random. What is the probability that a specific student is chosen?
8.
What is the probability of selecting the letter "e" from the word "elephant"?
