Curriculum Alignment
- Strand
- 3.0 Statistics and Probability
- Sub-Strand
- 3.2 Probability 1
- Specific Learning Outcomes
Subsection 3.2.7 Probability in Real-Life
Teacher Resource 3.2.46.
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 3.2.9.
Work in groups
Grade \(10\) learners went on a field trip to a weather station to learn about how meteorologists use probability to predict the weather.
The weather forecast says: There is a \(70\%\) chance of rain tomorrow.
(a)
What does \(70\%\) probability mean?
(b)
Should students carry an umbrella? Why?
(c)
Does \(70\%\) probability guarantee that it will rain? Explain your answer.
(d)
What could happen if you ignore the probability?
(e)
How do people use probability in daily life without realising it?
(f)
Share your work with the class.
Key Takeaway 3.2.47.
Probability is used in real-life situations to make predictions and informed decisions.
For example,
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In weather forecasting, meteorologists use probability to predict the likelihood of rain, sunshine, or storms.
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In sports, coaches and analysts use probability to assess the chances of winning a game or making a successful play.
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In quality control, manufacturers use probability to determine the likelihood of defects in their products and to improve their production processes.
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In traffic management, authorities use probability to analyze traffic patterns and make decisions about road construction and traffic light timing.
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In gambling, players use probability to calculate the odds of winning a bet or a lottery.
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In healthcare, doctors use probability to assess the risk of diseases and determine the best treatment options for patients.
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In finance, investors use probability to evaluate the potential returns and risks of different investments.
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In elections, political analysts use probability to predict the outcome of elections based on polling data and historical trends.
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In everyday decision-making, individuals use probability to assess the risks and benefits of various choices, such as whether to carry an umbrella or not based on the chance of rain.
By applying the concepts of probability, we can better understand and navigate the uncertainties of the world around us, making more informed decisions in our personal and professional lives.
Example 3.2.48.
A class of \(30\) students is planning a revision session for their upcoming exams. They have three time slots to choose from: \(4\) PM, \(5\) PM, and \(6\) PM. The students were asked to vote for their preferred time slot, and the results are as follows:
Based on the votes, determine the probability of each time slot being chosen for the revision session.
Solution.
To find the probability of each time slot being chosen, we divide the number of votes for each time slot by the total number of students (\(30\)).
Therefore, the probabilities of each time slot being chosen are:
Example 3.2.49.
A weather forecast predicts a \(60\%\) chance of rain tomorrow. If you have an outdoor event planned, what is the probability that it will not rain?
Example 3.2.50.
A bag contains \(5\) red balls, \(3\) blue balls, and \(2\) green balls. If you randomly draw one ball from the bag, what is the probability of drawing a red ball?
Example 3.2.51.
A student is taking a multiple-choice test with \(4\) questions, each having \(3\) possible answers (A, B, C). If the student guesses on all questions, what is the probability of getting at least one question correct?
Solution.
The probability of getting a question wrong is \(\frac{2}{3}\) (since there are \(2\) incorrect answers out of \(3\)).
The probability of getting all \(4\) questions wrong is \(\left(\frac{2}{3}\right)^4 = \frac{16}{81}\text{.}\)
Therefore, the probability of getting at least one question correct is \(1 - \frac{16}{81} = \frac{65}{81} \approx 0.80\%\text{.}\)
Exercises Exercise
1.
A weather report states that the probability of rain is \(0.8\text{.}\)
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Should farmers prepare for rainfall?
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Explain your answer.
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Does \(0.8\) mean it will definitely rain?
Answer.
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Yes, farmers should prepare for rainfall.
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A probability of \(0.8\) means there is an \(80\%\) chance of rain, which is a high likelihood. It is advisable for farmers to take precautions to protect their crops and livestock from potential rainfall.
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No, a probability of \(0.8\) does not guarantee that it will rain. It indicates a high likelihood, but there is still a \(20\%\) chance that it may not rain.
2.
In a manufacturing factory, the probability that a product is defective is \(0.02\text{.}\)
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What does \(0.02\) mean?
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Out of \(100\) products, how many are expected to be defective?
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Why is probability important in quality control?
Answer.
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Probability is important in quality control because it helps manufacturers assess the likelihood of defects and take measures to reduce them, ensuring that products meet quality standards and customer satisfaction.
3.
A school records that the probability a student arrives late is \(0.15\text{.}\)
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What is the probability that a student arrives on time?
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If there are \(200\) students, how many are expected to arrive late?
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Suggest one strategy the school could use to reduce lateness.
Answer.
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The probability that a student arrives on time is \(1 - 0.15 = 0.85 (85\%)\text{.}\)
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One strategy the school could use to reduce lateness is to implement a reward system for students who consistently arrive on time, such as giving out small prizes.
