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 happen***Total 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 = *1***6**

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) = *2***6** = *1***3**

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") = *4***6** = *2***3**

Let us include them:

P(A) + P(A") = *1***3** + *2***3** = *3***3** = 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") = *6***36** = *1***6**

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")**