Probability

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

1. Introduction to Probability

• Probability is used to measure uncertainty.
• It is widely used in games, weather forecasting, insurance, and many real-life situations.
• The value of probability ranges from 0 (impossible event) to 1 (certain event).

2. Key Terms

• Experiment: An action or process that leads to one or more outcomes (e.g., tossing a coin).
• Outcome: The result of an experiment (e.g., getting heads).
• 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:

0 ≤ P(A) ≤ 1

4. Examples

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

5. Important Points

• The probability of an impossible event is 0.
• The 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. Practice Questions

1. What is the probability of getting a tail when tossing a coin?
2. What is the probability of getting a number less than 5 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. If a card is drawn from a deck of 52 cards, what is the probability of getting a king?

7. 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.
• Probability is used in many real-life situations to make predictions and informed decisions.