Introduction to probability Revision Notes

Probability measures how likely an event is to happen, with values ranging from 0 to 1. A probability of 0 means the event cannot occur, while a probability of 1 means the event is certain to occur.

For example, the probability of rolling a 7 on a standard six-sided die is 0 because 7 is not a possible outcome. Conversely, the probability of rolling a number less than 7 is 1 because all outcomes (1 to 6) satisfy this condition.

Probabilities can be expressed as fractions, decimals, or percentages. For instance, a probability of 0.5 can also be written as 1/2 or 50%.

• Probability values range from 0 (impossible) to 1 (certain).
• Probabilities can be fractions, decimals, or percentages.
• Understanding the scale helps interpret likelihoods correctly.

The probability of an event A occurring is written as P(A). The probability that event A does not occur is called the complement of A and is written as P(A').

The sum of the probabilities of an event and its complement is always 1, because either the event happens or it does not.

This relationship is expressed as: P(A) + P(A') = 1, which can be rearranged to find the complement: P(A') = 1 - P(A).

• P(A) denotes the probability of event A.
• P(A') denotes the probability of event A not occurring (complement).
• P(A) + P(A') = 1, so P(A') = 1 - P(A).

To calculate the probability of a single event, divide the number of favourable outcomes by the total number of possible outcomes, assuming all outcomes are equally likely.

For example, when flipping a fair coin, the probability of getting heads is 1 favourable outcome (heads) divided by 2 possible outcomes (heads or tails), so P(heads) = 1/2 = 0.5 = 50%.

Probabilities can also be calculated from data presented in tables, graphs, or Venn diagrams by identifying the number of outcomes that satisfy the event and dividing by the total number of outcomes.

• Probability = (Number of favourable outcomes) / (Total number of outcomes).
• Use data from tables, graphs, or Venn diagrams to count outcomes.
• Express answers as fractions, decimals, or percentages.

Consider a table showing the favourite fruit of 50 students:

| Fruit | Number of Students | |---------|--------------------| | Apples | 20 | | Bananas | 15 | | Oranges | 15 |

To find the probability that a randomly chosen student prefers bananas: P(bananas) = 15 / 50 = 0.3 = 30%. The probability that the student does not prefer bananas is P(bananas') = 1 - 0.3 = 0.7 = 70%.

• Identify the number of favourable outcomes from the data.
• Divide by the total number of outcomes.
• Calculate the complement by subtracting from 1.

Venn diagrams visually represent events and their relationships. To find the probability of a single event, count the number of outcomes inside the event's circle and divide by the total number of outcomes.

For example, if a Venn diagram shows 40 students, with 25 in circle A (students who play football), then P(A) = 25/40 = 0.625 = 62.5%. The probability that a student does not play football is P(A') = 1 - 0.625 = 0.375 = 37.5%.

• Count outcomes inside the event circle.
• Divide by total outcomes to find P(event).
• Use complement rule for P(event not occurring).