Lessons Grade 7

Chapter 7

Chapter 7: Probability

7.1 Introduction to Probability

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will certainly occur.

Formula:

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

7.2 Simple Probability

To calculate the probability of a simple event, divide the number of favorable outcomes by the total number of possible outcomes.

Example: If a fair die is rolled, the probability of getting a 3 is:

P(3)=16P(3) = frac{1}{6}P(3)=61​

7.3 Compound Probability

Compounding probability involves finding the probability of two or more events happening together. For independent events, the probability is the product of the individual probabilities.

Example: If you roll a fair die and flip a fair coin, the probability of rolling a 3 and getting heads is:

P(3 and heads)=P(3)×P(heads)=16×12=112P(text{3 and heads}) = P(3) times P(text{heads}) = frac{1}{6} times frac{1}{2} = frac{1}{12}P(3 and heads)=P(3)×P(heads)=61​×21​=121 Exercises

Exercise 1: Calculate the probability of the following events:

Rolling a 4 on a fair six-sided die.

Drawing a red card from a standard deck of 52 cards.

Getting heads when flipping a fair coin.

Rolling a number greater than 4 on a fair die.

Drawing a king from a standard deck of 52 cards.

Exercise 2: Calculate the compound probability for the following events:

Rolling a 2 on a fair die and getting tails on a fair coin.

Drawing a heart and a queen from a deck of cards (without replacement).

Rolling a number less than 3 and flipping heads.

Draw a red card and then a black card from a deck (without replacement).

Rolling a 5 on a die and then a 6 on a second die.