Probability

1. Random Experiments

An experiment when repeated under identical condition does not produce the same result every time but outcome is one of the several possible outcomes, then such an experiment is known as a random experiment. For example, before rolling a die we do not know the result, but after the experiment, the result of the random experiment is known.

An outcome is a result of a random experiment, this is also known as an event. The set of all possible outcomes is called the  sample space.

Tossing a coin, sample space: \(S = \{ H,\;T\} \)

Tossing 2 coins, sample space: \(S = \{ HH,\;TH,HT,\,TT\} \)

Tossing a coin and rolling a dice, sample space: \(S = \{ H1,\;H2,\;H3,\;H4,\;H5,\;H6,\;T1,\,T2,\,T3,\,T4,\,T5,\,T6\} \)

Example 01: Three dice are rolled together, how many elements are there in the sample space?

The number of elements in the sample space will be 6×6×6 = 216.