Lesson Notes By Weeks and Term v5 - Grade 10
Probability – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Probability – Week 1 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 10
Term: Term 4
Week: 1
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Probability is the measure of the likelihood that an event will occur. It’s a fundamental concept in mathematics with wide-ranging applications in everyday life. For South African learners, understanding probability can help make informed decisions about various aspects of their lives, from understanding weather forecasts and sports odds to analyzing financial risks and interpreting statistical data presented in the news regarding elections, unemployment rates, or disease outbreaks. Consider the lottery, for example. Understanding probability, even in a basic sense, can help you assess the likelihood of winning and make responsible decisions about participation.
2.1 Basic Terminology: Experiment: An activity with observable results. Examples include flipping a coin, rolling a die, drawing a card from a deck, or observing the weather each day for a month.
Outcome: A possible result of an experiment. For example, if you flip a coin, the possible outcomes are "Heads" or "Tails". If you roll a die, the possible outcomes are 1, 2, 3, 4, 5, or
6. Sample Space (S): The set of all possible outcomes of an experiment. We denote the sample space with the letter 'S'.
For example: Flipping a coin: S = {Heads, Tails} Rolling a die: S = {1, 2, 3, 4, 5, 6} Drawing a card from a standard deck (considering only the suit): S = {Hearts, Diamonds, Clubs, Spades} Event (E): A subset of the sample space. It’s a specific outcome or a set of outcomes that we are interested in.
For example: Rolling an even number on a die: E = {2, 4, 6} Drawing a red card from a standard deck: E = {Hearts, Diamonds} Equally Likely Outcomes: Outcomes that have the same chance of occurring. A fair coin has equally likely outcomes (Heads or Tails). A fair die has equally likely outcomes (1, 2, 3, 4, 5, or 6). 2.2 Calculating Probability: The probability of an event (E), denoted by P(E), is calculated using the following formula, provided that all outcomes in the sample space are equally likely: P(E) = Number of favourable outcomes in E / Total number of possible outcomes in S P(E) = n(E) / n(S) (where n(E) is the number of outcomes in event E, and n(S) is the number of outcomes in the sample space S) Probability is always a number between 0 and 1 (inclusive): 0 ≤ P(E) ≤
1. P(E) = 0 means the event is impossible. P(E) = 1 means the event is certain to occur. 2.3
Examples: Example 1: Rolling a Die What is the probability of rolling a 4 on a fair six-sided die?
Experiment: Rolling a die.
Sample Space (S): {1, 2, 3, 4, 5, 6} Therefore, n(S) = 6 Event (E): Rolling a
4. E = {4} Therefore, n(E) = 1 Probability: P(E) = n(E) / n(S) = 1/6 Therefore, the probability of rolling a 4 is 1/
6. We can also express this as a decimal (approximately 0.167) or a percentage (approximately 16.7%).
Example 2: Drawing a Card A standard deck of playing cards has 52 cards. What is the probability of drawing an Ace?
Experiment: Drawing a card from a deck.
Sample Space (S): All 52 cards.
Therefore, n(S) = 52 Event (E): Drawing an Ace. There are 4 Aces (one of each suit). E = {Ace of Hearts, Ace of Diamonds, Ace of Clubs, Ace of Spades}.
Therefore, n(E) = 4 Probability: P(E) = n(E) / n(S) = 4/52 = 1/13 Therefore, the probability of drawing an Ace is 1/
1
3. Example 3: The Soccer Team A soccer team in Soweto has 11 players. They decide to choose a captain randomly by drawing names from a hat. What is the probability that Thando will be chosen as captain?
Experiment: Drawing a name from a hat.
Sample Space (S): All 11 players' names.
Therefore, n(S) = 11 Event (E): Thando's name is drawn. E = {Thando}.
Therefore, n(E) = 1 Probability: P(E) = n(E) / n(S) = 1/11 Therefore, the probability of Thando being chosen as captain is 1/
1
1. Example 4: Marbles in a Bag A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble from the bag?
Experiment: Drawing a marble from the bag.
Sample Space (S): All marbles in the bag.
Therefore, n(S) = 5 + 3 + 2 = 10 Event (E): Drawing a blue marble. There are 3 blue marbles.
Therefore, n(E) = 3 Probability: P(E) = n(E) / n(S) = 3/10 Therefore, the probability of drawing a blue marble is 3/
1
0. Guided Practice (With Solutions)
Question 1: A spinner has 8 equal sections, numbered 1 to
8. What is the probability of spinning an odd number?
Solution: Experiment: Spinning the spinner.
Sample Space (S): {1, 2, 3, 4, 5, 6, 7, 8}.
Therefore, n(S) = 8 Event (E): Spinning an odd number. E = {1, 3, 5, 7}.
Therefore, n(E) = 4 Probability: P(E) = n(E) / n(S) = 4/8 = 1/2
Commentary: We first identified the total number of outcomes (the sample space) and then the number of favourable outcomes (the odd numbers). We then applied the formula to calculate the probability.
Question 2: A box contains 12 chocolates: 4 milk chocolates, 5 dark chocolates, and 3 white chocolates. If you randomly select a chocolate, what is the probability of selecting a dark chocolate?
Solution: Experiment: Selecting a chocolate.
Sample Space (S): All 12 chocolates.
Therefore, n(S) = 12 Event (E): Selecting a dark chocolate. There are 5 dark chocolates.
Therefore, n(E) = 5 Probability: P(E) = n(E) / n(S) = 5/12
Commentary: This example reinforces the importance of identifying the total number of possibilities (total number of chocolates) and the specific outcome we are interested in (dark chocolates).
Question 3: What is the probability of rolling a number greater than 2 on a standard six-sided die?
Solution: Experiment: Rolling a die.
Sample Space (S): {1, 2, 3, 4, 5, 6}.
Therefore, n(S) = 6 Event (E): Rolling a number greater than
2. E = {3, 4, 5, 6}.