Lesson 2 of 11 · 7 min
Occurrence and types of events
NCERT §14.1.1, §14.1.2
A visitor tosses the three coins and gets HTT. Did the event 'at least one head' happen? Did 'exactly two heads' happen? The coins show only one outcome, but many events are being judged at once.
The lesson in notes
In short
An event E is said to occur when the actual outcome ω of the experiment lies in E, that is ω ∈ E. If ω ∉ E, the event has not occurred.
Throw a die with E = 'a number less than 4'. If 1, 2 or 3 turns up, E has occurred; if 5 turns up, it has not.
Impossible event: φ, the empty subset. On a die, 'the number is a multiple of 7' has no outcome in it, so it is φ.
Sure event: S itself. On a die, 'the number is odd or even' contains every outcome, so it is S and must occur.
Simple (elementary) event: a subset with exactly one sample point. A sample space of n distinct outcomes has exactly n simple events; for two coin tosses they are {HH}, {HT}, {TH} and {TT}.
Compound event: a subset with more than one sample point. With three coins, 'exactly one head' = {HTT, THT, TTH}, 'at least one head' has 7 points and 'at most one head' = {TTT, THT, HTT, TTH}; all three are compound.
Mela stall (made up): 'at least one head' on three coins holds 7 of the 8 outcomes; only TTT is left out.