Concept 14.1

Count Equally Likely Outcomes

Source: NCERT Mathematics, Class 1010 minute lesson

Formal statement

The theoretical probability of an event E is P(E) = (number of outcomes favourable to E) / (number of all possible outcomes), provided the outcomes are equally likely.

The intuition

Throw two dice. The possible sums are 2 to 12, eleven of them, but they are not equally likely: there is one way to get 2 and six ways to get 7.

So count the 36 ordered pairs, which are equally likely, not the 11 sums. P(sum 7) = 6/36 = 1/6, not 1/11.

The attention

Look at whether the outcomes you're counting are equally likely.

P(sum = 7) = 6 / 36 ordered pairs not 1 / 11 possible sums

Look hereNot here

Look here: Outcomes that are equally likely. The formula only works over equally likely outcomes. For two dice, those are the 36 ordered pairs.
Not here: Outcomes that aren't. The 11 sums are possible results, but 7 happens six times as often as 2. Counting them equally gives wrong answers.
What it teaches: Before you count, check that every thing you count has the same weight.