Concept 14.3
Every Probability Lies Between 0 and 1
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
The probability of an event lies between 0 and 1: 0 ≤ P(E) ≤ 1. An impossible event has probability 0 and a sure (certain) event has probability 1.
The intuition
The favourable outcomes are a part of all the outcomes. A part can be none of the whole or all of it, never more and never less.
So any probability above 1 or below 0 is a signal that something was counted wrong, usually that the favourable outcomes weren't drawn from the same list as the total.
The attention
Look at the favourable outcomes as a part of the whole.
P = favourable / all outcomes, so 0 ≤ P ≤ 1; an answer like 7/6 means a counting error
Look hereNot here
- Look here
- The favourable outcomes, a part of the whole. Favourable outcomes are chosen from the list of all outcomes, so they can't outnumber it.
- Not here
- An answer outside 0 to 1. An answer like 7/6 can come out of careless counting. Accepting it skips the one check every probability must pass.
- What it teaches
- Know the range an answer must fall in. It catches mistakes for free.