Revision: Probability Mathematics SSLC (English Medium) Class 9 Tamil Nadu Board of Secondary Education

The outcomes satisfying a particular condition are called favourable outcomes.

A set of favourable outcomes of a given sample space is an ‘event’. Event is a subset of the sample space.

• Events are denoted by capital letters A, B, C, D etc.
• The number of elements in event A is written n(A).
• Since A ⊆ S, always 0 ≤ n(A) ≤ n(S).
• Example: two coins tossed, A = getting at least one tail → A = {TT, TH, HT}, n(A) = 3.

In Mathematical language, when possibility of an expected event is expressed in number, it is called ‘Probability’. It is expressed as a fraction or percentage using the following formula.

\[ P(A) = \frac{\text{Number of sample points in event } A}{\text{Number of sample points in sample spaces}} = \frac{n(A)}{n(S)} \]

• The Probability is expressed as a fraction or a percentage.
• The probability of any event is from \[ 0 \text{ to } 1 \text{ or } 0\% \text{ to } 100\%. \]
• If \[ E \] is any event, \[ 0 \leq P(E) \leq 1 \text{ or } 0\% \leq P(E) \leq 100\%. \]

• The sample space \[ S \] contains all possible outcomes.
• An event is a subset of the sample space.
• A simple event has one outcome; a compound event has more than one outcome.
• A certain event has probability \[ 1; \] an impossible event has probability \[ 0. \]
• The complement of \[ A \] is \[ A', \] and \[ P(A') = 1 - P(A). \]
• Mutually exclusive events cannot occur together: \[ A \cap B = \varnothing. \]
• Exhaustive events together cover the entire sample space: \[ A \cup B = S. \]
• For equally likely outcomes, \[ P(A) = \frac{n(A)}{n(S)}. \]
• For any two events, \[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \]

1. Probability = possibility of an expected event expressed in number.
2.  \[ P(A) = n(A) / n(S). \]
3. Expressed as a fraction or a percentage.
4. \[ 0 \leq P(E) \leq 1, \] i.e. \[ 0\% \text{ to } 100\%. \]