Concept 14.2
Count the Opposite Event
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
For any event E, P(E) + P(not E) = 1, so P(not E) = 1 − P(E). E and 'not E' are complementary events.
The intuition
'At least one head in three tosses' has seven favourable outcomes out of eight. Listing them is slow and easy to get wrong.
Its opposite, 'no heads', has exactly one: TTT. So P(at least one head) = 1 − 1/8 = 7/8. When the event is crowded, count its opposite.
The attention
Look at the opposite event when the event itself is crowded.
P(at least one head) = 1 − P(no heads) instead of listing all 7 outcomes
Look hereNot here
- Look here
- The opposite event. 'No heads' has one outcome. 1 − 1/8 = 7/8, in one line.
- Not here
- Counting the event directly. Listing 7 outcomes works, but it's slow and one missed case breaks the answer.
- What it teaches
- When something is hard to count, count what it isn't.