Probability

Grade 10 Math - Probability

Lesson Objectives

Understand the basic concepts of probability.
Define outcomes, sample space, and events.
Calculate simple probabilities using coins and dice.
Apply the formula: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$
Solve basic probability problems involving real-life scenarios and past exams.

Lesson Introduction

Probability is the measure of how likely an event is to happen. It ranges from 0 (impossible) to 1 (certain). In this lesson, we will explore basic probability through familiar activities like tossing coins and throwing dice, and learn how to determine the likelihood of various outcomes.

Core Lesson Content

Basic Terms in Probability

Experiment: An action or process that leads to a set of outcomes (e.g., tossing a coin).
Outcome: A possible result of an experiment (e.g., Head).
Sample Space (S): The set of all possible outcomes.
Event: A subset of the sample space.

Formula for Probability

$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Worked Example

Example 1: A coin is tossed. What is the probability of getting a head?
Sample space:

S = \{H, T\}

Number of favorable outcomes = 1

P(H) = \frac{1}{2}

Example 2: A die is thrown. What is the probability of getting a 5?

S = \{1, 2, 3, 4, 5, 6\}

P(5) = \frac{1}{6}

Example 3: Find the probability of getting an even number when a die is thrown.
Even outcomes =

\{2, 4, 6\}

P(\text{even}) = \frac{3}{6} = \frac{1}{2}

Example 4: A coin is tossed twice. What is the probability of getting two heads?

S = \{HH, HT, TH, TT\}

P(HH) = \frac{1}{4}

Example 5: A number is picked at random from 1 to 5. Find the probability that it is greater than 3.
Favorable outcomes: 4, 5 → 2 outcomes

P(x > 3) = \frac{2}{5}

Example 6: A letter is chosen at random from the word "MATH". What is the probability of selecting a vowel?
Vowels: A → 1 favorable

P(\text{vowel}) = \frac{1}{4}

Example 7: What is the probability of not getting a 3 when a die is rolled?
Favorable outcomes = 1, 2, 4, 5, 6 → 5

P(\text{not 3}) = \frac{5}{6}

Example 8: Two coins are tossed. What is the probability of getting at least one head?

S = \{HH, HT, TH, TT\}

, favorable = HH, HT, TH → 3

P(\geq 1\text{ head}) = \frac{3}{4}

Example 9: A bag contains 2 red, 3 blue, and 5 green balls. Find the probability of selecting a green ball.
Total = 10, green = 5

P(\text{green}) = \frac{5}{10} = \frac{1}{2}

Example 10: A card is chosen from a pack of 52 cards. Find the probability of drawing an ace.
There are 4 aces in a pack.

P(\text{ace}) = \frac{4}{52} = \frac{1}{13}

Exercises

A coin is tossed. What is the probability of getting a tail?
A die is thrown. What is the probability of getting a number less than 5?
What is the probability of getting an odd number when a die is rolled?
[WAEC] If a coin is tossed three times, what is the probability of getting at least one head? (Past Question)
In the word "PROBABILITY", find the probability of choosing a vowel at random.
[NECO] A bag contains 3 red, 2 blue, and 5 yellow balls. What is the probability of selecting a red ball? (Past Question)
If a number is chosen from 1 to 10, what is the probability that it is a prime?
[JAMB] A number is picked at random from 1 to 20. What is the probability that it is a multiple of 4? (Past Question)
Two dice are rolled. What is the probability that the sum is 7?
A spinner has 5 equal sectors numbered 1 to 5. What is the probability it lands on an even number?

Conclusion/Recap

We explored the basic ideas of probability using familiar activities. You learned how to calculate probabilities using coins, dice, and other simple methods. In future lessons, we will cover compound events and use of tree diagrams to model probabilities.