# Stat Chapter 2 Prob 4527661

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### Probability:

Probability Sample Space Diagrams

### Sample Space:

Sample Space A Sample Space is a LIST of all possible outcomes. A Sample Space Diagram is a TABLE which shows all the possible outcomes of a scenario.

### e.g. Sample space diagram for rolling a die and tossing a coin:

e.g. Sample space diagram for rolling a die and tossing a coin Dice 1 2 3 4 5 6 Coin H T

### Independent Events:

Independent Events Events are independent if the outcome of each event is not affected by any other event outcomes.

### Example:

Example A bag contains 2 blue, 3 green and 5 red balls. If I draw one ball at random probability of a blue ball … = 2/10 If I draw another ball the probability of it being Blue depends on what colour ball was drawn first – not independent .

### Probability - Notation:

Probability - Notation The probability of an event A happening can be written as P(A) P(A) = number of ways event A can happen total number of ways possible including event A

### Example:

Example The probability of getting an “Ace” by drawing one card from a pack of 52 cards: P(Ace) = number of ways of getting an ace total number of possible cards = 4 52

### Probability of Event NOT happening:

Probability of Event NOT happening P(A’) is probability of event A NOT happening. P(A’) = 1 – P(A) e.g. P(not an ace) = 1 – 4 = 48 52 52

### Probability of Independent Events:

Probability of Independent Events If two events A and B are independent then the probability of them both happening is: P(A and B) = P(A) x P(B)

### Example:

Example A dice and a coin are thrown. What is the probability of a HEAD and a 4 ? Answer: P(H and 4) = P(H) x P(4) = 1/2 x 1/6 = 1/12

### Mutually Exclusive:

Mutually Exclusive Events are mutually exclusive if they can’t happen at the same time e.g. If coin is tossed it cannot land as HEAD and TAIL Events “showing a head” and “showing a tail” are mutually exclusive.

### Probability of Mutually Exclusive:

Probability of Mutually Exclusive If two events A and B are mutually exclusive the probability of either event A or event B occurring … P(A or B) = P(A) + P(B)

### Example:

Example If a dice is thrown what is the probability of an even number or a “3” Since three is not an even number (!) P(Even or “3”) = P(Even) + P(3) = 3/6 + 1/6 = 4/6 