Lesson Notes By Weeks and Term v5 - Grade 10
Probability: basic concepts and simple experiments – Week 8 focus
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Probability: basic concepts and simple experiments – Week 8 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematical Literacy
Class: Grade 10
Term: Term 4
Week: 8
Theme: General lesson support
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Probability is the study of how likely events are to happen. It's all about chance and uncertainty. Understanding probability is vital in everyday life, from deciding whether to buy a lottery ticket to assessing the risks associated with driving, to understanding weather forecasts. In South Africa, a good grasp of probability can empower us to make informed decisions about personal finances (like insurance), health (understanding medical test results), and even understanding the fairness of games of chance. It’s also important for understanding the statistics presented in news reports, allowing us to be more critical consumers of information.
2.1 Basic Terminology: Experiment: An activity with observable results. Examples include tossing a coin, rolling a die, or drawing a card from a deck.
Outcome: A possible result of an experiment. For example, when tossing a coin, the possible outcomes are "Heads" or "Tails." Sample Space: The set of all possible outcomes of an experiment. We usually denote the sample space with the letter 'S'. For example, the sample space when rolling a six-sided die is S = {1, 2, 3, 4, 5, 6}.
Event: A specific outcome or a set of outcomes from an experiment. For example, rolling an even number on a die is an event, and it corresponds to the outcomes {2, 4, 6}.
Probability: A measure of how likely an event is to occur. It is expressed as a number between 0 and 1 (inclusive), where 0 indicates impossibility and 1 indicates certainty. 2.2 Calculating Probability: The basic formula for calculating the probability of an event is: P(Event) = (Number of favourable outcomes) / (Total number of possible outcomes)
Where: P(Event) represents the probability of the event occurring. Number of favourable outcomes refers to the number of outcomes that satisfy the event. Total number of possible outcomes refers to the total number of outcomes in the sample space. 2.3 Expressing Probability: Probability can be expressed in three ways: Fraction: e.g., 1/2 (one out of two)
Decimal: e.g., 0.5 (equivalent to 1/2)
Percentage: e.g., 50% (equivalent to 0.5 and 1/2) To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100. 2.4 Certain, Likely, Unlikely, and Impossible Events: Certain Event: An event that will definitely occur. Its probability is 1 (or 100%).
Example: The sun will rise tomorrow.
Likely Event: An event that has a high chance of occurring. Its probability is closer to
1. Example: South Africa winning a cricket match against a weaker team.
Unlikely Event: An event that has a low chance of occurring. Its probability is closer to
0. Example: Winning the Lotto jackpot.
Impossible Event: An event that cannot occur. Its probability is 0 (or 0%).
Example: Rolling a 7 on a standard six-sided die. 2.5 Worked
Examples: Example 1: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?
Event: Selecting a blue marble.
Number of favourable outcomes: 3 (since there are 3 blue marbles).
Total number of possible outcomes: 5 + 3 + 2 = 10 (total number of marbles).
Therefore, P(Blue marble) = 3/10 = 0.3 = 30%.
Example 2: What is the probability of rolling an odd number on a standard six-sided die?
Event: Rolling an odd number.
Number of favourable outcomes: 3 (the odd numbers are 1, 3, and 5).
Total number of possible outcomes: 6 (the numbers on the die are 1, 2, 3, 4, 5, and 6).
Therefore, P(Odd number) = 3/6 = 1/2 = 0.5 = 50%.
Example 3: A spinner has 4 equal sections colored red, blue, green, and yellow. What is the probability of the spinner landing on red?
Event: Spinner landing on red.
Number of favourable outcomes: 1 (since there is only one red section).
Total number of possible outcomes: 4 (since there are four sections).
Therefore, P(Red) = 1/4 = 0.25 = 25%. Guided Practice (With Solutions)
Question 1: A coin is tossed. What is the probability of getting heads?
Solution: Event: Getting heads.
Number of favourable outcomes: 1 (there is only one "heads" side).
Total number of possible outcomes: 2 (heads or tails).
Therefore, P(Heads) = 1/2 = 0.5 = 50%. This is a classic example of an equally likely event.
Question 2: A number is chosen randomly from the numbers 1 to 20 (inclusive). What is the probability that the number is a multiple of 5?
Solution: Event: Choosing a multiple of
5. Favourable Outcomes: 5, 10, 15, 20 (4 numbers)
Total number of possible outcomes: 20 (numbers 1 to 20).
Therefore, P(Multiple of 5) = 4/20 = 1/5 = 0.2 = 20%. We simplify the fraction where possible.
Question 3: A box contains 8 apples and 12 oranges. What is the probability of picking an orange at random?
Solution: Event: Picking an orange.
Number of Favourable Outcomes: 12 (12 oranges)
Total Number of Possible Outcomes: 8 + 12 = 20 (total fruit) Therefore, P(Orange) = 12/20 = 3/5 = 0.6 = 60%. Always check to simplify your fractions.
Question 4: In a class of 30 learners, 18 are girls and 12 are boys. If a learner is chosen at random, what is the probability that the learner is a girl?
Solution: Event: Choosing a girl.
Number of favourable outcomes: 18 (number of girls)
Total number of possible outcomes: 30 (total number of learners) Therefore, P(Girl) = 18/30 = 3/5 = 0.6 = 60%. This shows how probability can be used to represent proportions within a group. Independent Practice (Questions Only) A bag contains 7 yellow sweets, 5 red sweets and 3 green sweets. What is the probability of picking a red sweet? A die is rolled. What is the probability of rolling a number greater than 4?