# probabilities and combinations a quick guide

Probabilites and combinations are very difficult for me understand because i always keep forgetting what they mean.

lets start with some basic examples.

__ Example 1: __

What is the probality that we will get `head`

when we flip the coin

```
formula 1
P(h) = No. of posssible outcomes that meat our condition/ All possible conditions
```

solution

`P(h) = 1/2(head+tail)`

__ Example 2: __

What is the posssibity that we will get number less than 4 when roll a dice.

```
p(answer) = 3(that can be 1, 2 and 3 on the dice)/ 6(total outcome of dice)
```

__ Example 3: __

There are some cases we need van-diagram to solve the problem like ** Scenerio ** if there are 4 red dice, 3 red cube and 4 yellow cube then

What is the probality to get red cube

```
P = 3/11
```

__ Example 4: __ compound outcome

You’re playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.

If you randomly choose your character and tool, what is the probability that you won’t be a hobbit or use an umbrella?

There are \blue 3 character choices and \pink 5 choices for the tool, so there are \blue3\times\pink5=3×5=15 total possible combinations. If we pick randomly, all the combinations are equally likely. here are 8 favorable combinations.

so

```
P = 8/15
```

__ Example 5: __

There are some question needed tree view like this.

One more question for the practice

Futher reading - Combinations and Permutations - Better explanation of C&P