Types of Events

Event means one (or more) outcomes.

An event with only one outcome: - Getting a Tail when tossing a coin is an event - Rolling a "5" is an event.

An event with several outcomes: - Choosing a "King" from a deck of cards (any of the 4 Kings) - Rolling an "even number" (2, 4 or 6)

Types of Events

1. Independent

• Each event is NOT affected by any other events

• Example: Toss a coin three times and it comes up 'Head' each time. What is the chance of 'Tail' in the next toss? Answer: It is always 50%. Gambler's Fallacy: 'A tail is due' or'Just one more go, my luck is due'

2. Dependent

• An event can be affected by previous events

• Also called Conditional probability*

• Example: Chance of drawing a King 1st Attempt: 4 out of 52

  • If 1st card was a King, 2nd card has less chances to be King. 3/51

  • If 1st card was NOT a King, 2nd card has more chances to be King. 4/51

3. Mutually Exclusive

• Events that can't happen at the same time

• Example: Heads and Tails are Mutually Exclusive

Conditional Probability*

A conditional probability is the probability of an event, given some other event has already occurred. Example: A ball hit the red shelf (event A), what's the probability it also hit the blue shelf (event B)? Refer to the visual explanation at Setosa.io

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$

Link: - MathsIsFun: Types of Events - Setosa.io: Conditional probability