Learn Class 11 Math - Probability

Probability is a numerical measure of the degree of uncertainty in various situations. It can have a positive value ranging from 0 to 1.

The words 'probably,' 'doubt, "most probably,' 'chances,' and so on all have ambiguous meanings.

Probability equals the number of times a favorable event occurs. the total number of outcomes

Probability Approaches:

• Statistical approach: Data gathering and observation
• Classical approach: Only equally likely events are considered.
• Axiomatic technique: This method is used in real-life circumstances. It is closely related to set theory.

Experiments at Random:

• A variety of outcomes are possible.
• Knowing the outcome in advance is impossible.

Outcomes:

An outcome is the most likely outcome of a random experiment.

A random experiment has the possibility of producing various outcomes, which is known as sample space. It's represented by the letter S. When a coin flips, for example, the winner is determined by the head.

A sample point is a name given to each member of the sample space. For example, in a coin flip, the head is a sample point.

Event:

• A series of favorable outcomes is referred to as an event.
• A subset E of a sample space S is defined as an event.
• Consider what happens if you roll a dice and get an unexpected outcome.

The occurrence of a specific event:

If the experiment's outcome is that E occurs in a sample space S, E is said to have happened. If the outcome is such that E did not happen, we say that E did not occur.