Lesson Notes By Weeks and Term v5 - Grade 10
Probability – Week 5 focus
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Probability – Week 5 focus
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Subject: Mathematics
Class: Grade 10
Term: Term 4
Week: 5
Theme: General lesson support
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Probability is a fundamental branch of mathematics that deals with the likelihood of an event occurring. Understanding probability is crucial in many aspects of life, from making informed decisions about investments and insurance to interpreting weather forecasts and understanding the odds in sports. In a South African context, understanding probability can help learners make informed choices about participating in lotteries like the National Lottery (Lotto), understanding the risks associated with HIV/AIDS, or even analysing data related to local elections.
Probability: Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
Formula: P(Event) = Number of favourable outcomes / Total number of possible outcomes Sample Space (S): The sample space is the set of all possible outcomes of an experiment. For example, when flipping a coin, the sample space is {Heads, Tails}. When rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
Event: An event is a specific outcome or a set of outcomes from a sample space. For example, getting a "Heads" when flipping a coin is an event. Rolling an even number on a die (2, 4, or 6) is also an event.
Theoretical Probability: Theoretical probability is the probability of an event based on mathematical reasoning and the understanding of the sample space. It's what should happen, in theory.
Example: The theoretical probability of rolling a 4 on a six-sided die is 1/6 because there is one favourable outcome (rolling a 4) and six total possible outcomes (1, 2, 3, 4, 5, 6).
Experimental Probability: Experimental probability is the probability of an event based on conducting an experiment and observing the outcomes. It's what actually happens when you try something out.
Formula: P(Event) = Number of times the event occurs / Total number of trials
Example: If you flip a coin 100 times and get heads 55 times, the experimental probability of getting heads is 55/100 = 0.
5
5. Mutually Exclusive Events: Two events are mutually exclusive if they cannot occur at the same time.
Example: Rolling a 3 and rolling a 4 on a single roll of a die are mutually exclusive events.
Formula: If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B)
Non-Mutually Exclusive Events: Two events are non-mutually exclusive if they can occur at the same time.
Example: Drawing a heart and drawing a king from a deck of cards are non-mutually exclusive events because you can draw the King of Hearts.
Formula: If events A and B are non-mutually exclusive, then P(A or B) = P(A) + P(B) - P(A and B)
Complementary Events: The complement of an event A is the event that A does not occur.
Example: The complement of rolling a 4 on a die is not rolling a 4 (i.e., rolling a 1, 2, 3, 5, or 6).
Formula: P(A') = 1 - P(A), where A' is the complement of A. The sum of the probability of an event and its complement is always 1.
Example 1: Theoretical Probability
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble at random?
Solution:
Total number of marbles = 5 + 3 + 2 = 10
Number of blue marbles = 3
P(Blue Marble) = Number of blue marbles / Total number of marbles = 3/10 = 0.3
Example 2: Experimental Probability
A survey was conducted among 100 Grade 10 learners in a South African school to determine their favourite sport.
The results are as follows:
Rugby: 40 learners
Soccer: 35 learners
Cricket: 20 learners
Other: 5 learners