Probability | Class 11 Mathematics Notes

14.1 Event

This section introduces the fundamental concept of an event in probability theory, building upon the earlier notions of random experiments and sample spaces. A random experiment is an action or process that leads to one of several possible outcomes, which are collectively represented by the sample space S. Each outcome is a sample point in S. An event is defined as any subset of the sample space, representing a collection of outcomes of interest. For example, consider the experiment of tossing a coin twice. The sample space is S = {HH, HT, TH, TT}, where H and T denote heads and tails respectively. An event E could be 'exactly one head appears', which corresponds to the subset E = {HT, TH} of S. This shows that events are subsets of the sample space and can range from single outcomes to multiple outcomes. The section further illustrates this with a table showing various event descriptions and their corresponding subsets of S, such as the event 'number of tails is exactly 2' corresponding to {TT}, or 'number of tails is more than two' corresponding to the empty set φ, which is an impossible event. This conceptualization of events as subsets of sample space is foundational for defining probabilities and analyzing random experiments.

📊 Diagram: Table on page 1 (7×2) showing descriptions of events and their corresponding subsets of sample space S.

🧪 Activity: Consider tossing a coin twice and identify subsets of the sample space corresponding to various event descriptions such as 'number of tails is exactly 2' or 'second toss is not head'.

🔗 Connection: This section sets the stage for understanding when an event occurs and different types of events, which are discussed in the following subsections.

Table on page 1 (7×2)

Table on page 18 (6×8)

Table on page 19 (4×5)

Table on page 23 (6×4)