Master Probability Concepts: Exhaustive, Favourable, Mutually Exclusive, and Equally Likely Cases

Welcome to the Data Science and AI Lecture Series brought to you by PostNetwork Academy.

Exhaustive Cases

The total number of possible outcomes in a random experiment is called exhaustive cases.

Examples:

• Tossing a coin: Sample Space \( S = \{H, T\} \)
• Number of Exhaustive Cases = \( 2 \).
• Throwing a die: Sample Space \( S = \{1, 2, 3, 4, 5, 6\} \)
• Number of Exhaustive Cases = \( 6 \).

Favourable Cases

Cases that lead to the happening of an event are called favourable cases.

Examples:

• Drawing a spade card from a deck: \( 13 \) spades.
• Getting an even number by throwing a die: \( \{2, 4, 6\} \).

Mutually Exclusive Cases

Cases are mutually exclusive if the occurrence of any one prevents the occurrence of all others in a single experiment.

Examples:

• Tossing a coin: Head and Tail are mutually exclusive.
• Drawing a card: Drawing a spade and a club are mutually exclusive.

Equally Likely Cases

Cases are equally likely if there is no reason to expect one outcome over the others.

Examples:

• Tossing an unbiased coin: Head and Tail are equally likely.
• Throwing an unbiased die: All six faces are equally likely.

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