Plus One Maths Notes Chapter 16 Probability

Plus One Maths Notes Chapter 16 Probability is part of Plus One Maths Notes. Here we have given Kerala 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 ∪ …… ∪ E_n = S, then we say that E₁, E₂, E₃, …….., E_n are exhaustive events.

If E₁ ∪ E₂ ∪ E₃ ∪ …… ∪ E_n = S, and E_i ∩ E_j = φ, i ≠ j then we say that E₁, E₂, E₃,…….., 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)

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