1. Introduction to Probability

Probability is the branch of mathematics that deals with the likelihood or chance of different outcomes. It helps us predict how likely an event is to happen.

• Probability is used in games, weather forecasts, insurance, and many real-life situations.
• It is a measure between 0 (impossible event) and 1 (certain event).

2. Basic Terms

• Experiment: An action or process that leads to one or more outcomes (e.g., tossing a coin).
• Trial: Each repetition of an experiment.
• Outcome: The result of a single trial (e.g., getting heads in a coin toss).
• Sample Space (S): The set of all possible outcomes (e.g., for a coin toss: S = {Heads, Tails}).
• Event: One or more outcomes of an experiment (e.g., getting an even number when rolling a die).

3. Calculating Probability

The probability of an event A is given by:

Probability is always a number between 0 and 1.

4. Examples

• Example 1: What is the probability of getting a head when tossing a coin?
  Sample space S = {Head, Tail}
  Number of favourable outcomes = 1 (Head)
  Total outcomes = 2
  P(Head) = 1/2
• Example 2: What is the probability of getting a 3 when rolling a die?
  Sample space S = {1, 2, 3, 4, 5, 6}
  Number of favourable outcomes = 1 (3)
  Total outcomes = 6
  P(3) = 1/6
• Example 3: What is the probability of getting an even number when rolling a die?
  Favourable outcomes = {2, 4, 6} (3 outcomes)
  Total outcomes = 6
  P(even) = 3/6 = 1/2

5. Important Points

• Probability of an impossible event is 0.
• Probability of a certain event is 1.
• The sum of probabilities of all possible outcomes of an experiment is 1.
• Probabilities are always between 0 and 1 (inclusive).

6. Common Mistakes

• Not listing all possible outcomes in the sample space.
• Counting the same outcome more than once.
• Forgetting that probability cannot be negative or greater than 1.

7. Practice Questions

1. What is the probability of getting a tail when tossing a coin?
2. What is the probability of getting a number greater than 4 when rolling a die?
3. A bag contains 3 red balls and 2 blue balls. What is the probability of picking a blue ball?
4. What is the probability of getting an odd number when rolling a die?
5. What is the probability of drawing a king from a standard deck of 52 cards?

8. Summary

• Probability measures how likely an event is to occur.
• P(A) = Number of favourable outcomes / Total number of possible outcomes.
• Probability values range from 0 to 1.
• Understanding probability helps in making predictions and informed decisions.