# Plus One Maths Notes Chapter 16 Probability

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:

1. Event ‘not A’ = A’
2. Event ‘A or B’ = A ∪ B
3. Event ‘A and B’ = A ∩ B
4. 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 E1 ∪ E2 ∪ E3 ∪ …… ∪ En = S, then we say that E1, E2, E3, …….., En are exhaustive events.

If E1 ∪ E2 ∪ E3 ∪ …… ∪ En = S, and Ei ∩ Ej = φ, i ≠ j then we say that E1, E2, E3,…….., En 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)