Probability+-+Types+of+Events

=Probability: Types of Events= //Events can be Independent, Mutually Exclusive or Conditional !//

Life is full of random events! You need to get a "feel" for them to be a smart and successful person. The toss of a coin, throw of a dice and lottery draws are all examples of random events.

Events
When we say "Event" we mean one (or more) outcomes. Example Events: An event can include several outcomes:
 * Getting a Tail when tossing a coin is an event
 * Rolling a "5" is an event.
 * Choosing a "King" from a deck of cards (any of the 4 Kings) **is also** an event
 * Rolling an "even number" (2, 4 or 6) is an event

Independent Events
Events can be "Independent", meaning each event is **not affected** by any other events. This is an important idea! A coin does not "know" that it came up heads before ... each toss of a coin is a perfect isolated thing. Example: You toss a coin three times and it comes up "Heads" each time ... what is the chance that the next toss will also be a "Head"? The chance is simply 1/2, or 50%, just like ANY OTHER toss of the coin. What it did in the past will not affect the current toss! Some people think "it is overdue for a Tail", but //really truly// the next toss of the coin is totally independent of any previous tosses. Saying "a Tail is due", or "just one more go, my luck is due" is called **The Gambler's Fallacy** (Learn more at [|Independent Events].)

Dependent Events
But some events can be "dependent" ... which means they **can be affected by previous events** ...

Example: Drawing 2 Cards from a Deck
After taking one card from the deck there are **less cards** available, so the probabilities change!

Let's say you are interested in the chances of getting a King. For the 1st card the chance of drawing a King is 4 out of 52 But for the 2nd card: This is because you are **removing cards** from the deck. Replacement: When you put each card **back** after drawing it the chances don't change, as the events are independent. Without Replacement: The chances will change, and the events are **dependent**. You can learn more about this at [|Dependent Events: Conditional Probability]
 * If the 1st card was a King, then the 2nd card is **less** likely to be a King, as only 3 of the 51 cards left are Kings.
 * If the 1st card was **not** a King, then the 2nd card is slightly **more** likely to be a King, as 4 of the 51 cards left are King.

Tree Diagrams
When you have Dependent Events it helps to make a "[|Tree Diagram]"

Example: Soccer Game
You are off to soccer, and love being the Goalkeeper, but that depends who is the Coach today: Sam is Coach more often ... about 6 of every 10 games (a probability of **0.6**).
 * with Coach Sam your probability of being Goalkeeper is **0.5**
 * with Coach Alex your probability of being Goalkeeper is **0.3**

Let's build the Tree Diagram! Start with the Coaches. We know 0.6 for Sam, so it must be 0.4 for Alex (the probabilities must add to 1): Then fill out the branches for Sam (0.5 Yes and 0.5 No), and then for Alex (0.3 Yes and 0.7 No): Now it is neatly laid out we could calculate probabilities (read more at "[|Tree Diagram]s").

Mutually Exclusive
It is either one or the other, but **not both** Examples: What isn't Mutually Exclusive Like here: Mutually Exclusive ||  || Hearts and Kings are Read more at [|Mutually Exclusive Events]
 * Mutually Exclusive** means you can't get both events at the same time.
 * Turning left or right are Mutually Exclusive (you can't do both at the same time)
 * Heads and Tails are Mutually Exclusive
 * Kings and Aces are Mutually Exclusive
 * Kings and Hearts are **not** Mutually Exclusive, because you can have a King of Hearts!
 * [[image:http://www.mathsisfun.com/data/images/set-aces-kings.gif width="211" height="140"]] ||  || [[image:http://www.mathsisfun.com/data/images/set-hearts-kings.gif width="187" height="140"]] ||
 * Aces and Kings are
 * not** Mutually Exclusive ||

=Reference=

@http://www.mathsisfun.com