We know that blowing air into a balloon, exceeding its capacity, leads to its bursting.
Such experiments are called deterministic experiments. In other words, we can determine the result of such experiments even before the start of such experiments.
What do you think the result would be if we toss a coin high in the air?
A coin has two faces: Head and Tail.
So, tossing a coin does not give us a definitive result.
We do not know the results until the experiment is carried out.
Such experiments are called random experiments.
Let us look at a few key terms associated with random experiments.
Some important terms
1. Trial: Each attempt of a random experiment is a trial.
In a random experiment of tossing a coin, if we have thrown the coin \(10\) times, then we have attempted \(10\) trials.
2. Outcome: The possible set of results at the end of each of the trials is an outcome.
Head is obtained as the outcome on the first attempt of tossing a coin.
3. Sample point: While a trial is conducted, each possible outcome is the sample point.
a. The sample points while tossing a coin is Head and Tail.
b. The sample points while rolling a die is \(1\), \(2\), \(3\), \(4\), \(5\) and \(6\).
4. Sample space: The collection of sample points is a sample space. The sample points in sample space is enclosed in curly braces. Sample space is denoted by \(S\). The number of points in a sample space is denoted by \(n(S)\).
a. The sample space of tossing of a coin:
\(S = \{H, T\}\)
\(n(S) = 2\)
b. The sample space of rolling a die
\(S = \{1, 2, 3, 4, 5, 6\}\)
\(n(S) = 6\)
5. Event: An event is a subset of a sample space.
The sample space of rolling a die, \(S = \{1, 2, 3, 4, 5, 6\}\)
An event of rolling a multiple of \(3\) is \(\{3, 6\}\).