Kerala State Board New Syllabus Plus One Maths Notes Chapter 16 Probability.

## Kerala Plus One Maths Notes Chapter 16 Probability

I. Random Experiments

An experiment is called a random experiment if it satisfies the following two conditions:

- It has more than one outcome.
- It is not possible to predict the outcome in advance.

Sample space: The set of all possible outcomes of a random experiment is called sample space. Generally denoted by S.

Event: Any subset E of a sample space S is called an event.

Types of Events:

1. Impossible event and sure event: The empty set φ and the sample space S describe the impossible event and sure event respectively.

2. Simple event: An event E having only one sample point of a sample space.

3. Compound event: An event having more than one sample point of a sample space.

Algebra of events:

- Event ‘not A’ = A’
- Event ‘A or B’ = A ∪ B
- Event ‘A and B’ = A ∩ B
- Event ‘A but not B’ = A ∩ \(\bar{B}\) = A – B

If A ∩ B = φ, then A and B are mutually exclusive events or disjoint events.

If E_{1} ∪ E_{2} ∪ E_{3} ∪ …… ∪ E_{n} = S, then we say that E_{1}, E_{2}, E_{3}, …….., E_{n} are exhaustive events.

If E_{1} ∪ E_{2} ∪ E_{3} ∪ …… ∪ E_{n} = S, and E_{i} ∩ E_{j} = φ, i ≠ j then we say that E_{1}, E_{2}, E_{3},…….., E_{n} are mutually exclusive events and exhaustive events.

II. Probability of an Event

Let S is a sample space and E be an event, such that n(S) = n and n(E) = m. If each outcome is equally likely, then it follows that P(E) = \(\frac{m}{n}\).

P(Impossible event) = 0 and P(Sure event) = 1, hence 0 ≤ P(E) ≤ 1.

If A and B are any two events, then P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

If A and B are mutually exclusive events, then P(A ∪ B) = P(A) + P(B)

If A is any events, then P(A’) = 1 – P(A)

P(A ∩ \(\bar{B}\)) = P(A) – P(A ∩ B)