 When the event is Heads, the enhance is Tails When the occasion is Monday, Wednesday the enhance is Tuesday, Thursday, Friday, Saturday, Sunday When the event is Hearts the complement is Spades, Clubs, Diamonds, Jokers

So the complement of an event is all the other outcomes (not the ones us want).

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And together the Event and also its enhance make all possible outcomes.

## Probability

Probability of an event happening = Number of ways it have the right to happenTotal number of outcomes

### Example: the possibilities of rolling a "4" v a die

Number of methods it can happen: 1 (there is just 1 face with a "4" top top it)

Total variety of outcomes: 6 (there room 6 faces altogether)

So the probability = 16

The probability of an event is presented using "P":

P(A) method "Probability of event A"

The enhance is displayed by a tiny mark ~ the letter such as A" (or periodically Ac or A):

P(A") method "Probability the the match of occasion A"

The 2 probabilities always include to 1

P(A) + P(A") = 1

### Example: roll a "5" or "6" Event A is 5, 6

Number of ways it have the right to happen: 2

Total number of outcomes: 6

P(A) = 26 = 13

The Complement of occasion A is 1, 2, 3, 4

Number of ways it deserve to happen: 4

Total number of outcomes: 6

P(A") = 46 = 23

Let us include them:

P(A) + P(A") = 13 + 23 = 33 = 1

Yep, that makes 1

It renders sense, right? Event A plus every outcomes that room not occasion A make up all possible outcomes.

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## Why is the match Useful?

It is sometimes less complicated to occupational out the enhance first. ### Example. Throw two dice. What is the probability the two scores are different?

Different scores are like getting a 2 and 3, or a 6 and also 1. That is a long list:

A = (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,3), (2,4), (1,5), (1,6),(3,1), (3,2), ... And so on !

But the enhance (which is once the two scores room the same) is only 6 outcomes:

A" = (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

And that is probability is:

P(A") = 636 = 16

Knowing that P(A) and P(A") with each other make 1, we can calculate:

 P(A) = 1 − P(A") = 1 − 16 = 56

So in this case (and plenty of others) the is much easier to work-related out P(A") first, then calculation P(A) = 1 − P(A")