# MATH 109 Lecture 5: 5.2 Stats: Finding Theoretical Probabilities, Mutually Exclusive Events

5.2

Finding Theoretical Probabilities

- Probability are always numbers between 0 and 1.

- 0 means that the event never

happens.

- 1 means that the event always

happens.

- 1- means that the event will not

happen.

Complement- “not event”

Equally Likely Outcomes- in some situations, all of the possible outcomes of a random

experiment occur with the same frequency.

-Example: when you flip a coin, heads and tails are equally likely; when you roll a die,

1,2,3,4,5, and 6 are all equally likely.

- When dealing with equally likely outcomes, it is sometimes helpful to list all of the

possible outcome.

Sample space- a list that contains all possible (and equally likely) outcomes.

- Represent the sample space with the letter s.

Event- any collection of outcomes in the sample space.

-Example: the sample space, s

, for rolling a die is the numbers, 1,2,3,4,5, and 6. The

event “get an even number” consist of the even outcomes in the sample space, s:

2,4,

and 6.

- Events are represented by uppercase letters: A,B,C, and so on …

Rule 1: A probability is always a number from 0 to 1 or (0% to 100%) inclusive (which means 0

and 1 are allowed). It may be expressed as a fraction, a decimal, or a percent.

0 P(A) 1≤ ≤

Rule 2: The probability that an event will not occur is 1 minus the probability that the event will

occur.

P(A does not occur) = 1 - P(A does occur)

P(Ac) = 1 - P(A)

The symbol Ac is used to represent the complement of A.

Rule 3: Probability of A = P(A) = Number of outcomes

Number of all possible outcomes

● This is true only for equally likely outcomes.

Ex 12: 10 Dice in a Bowl

Bowl contains:

- 5 red dice (5/10 or 50%)

- 3 green dice (3/10 or 30%)

- 2 white dice (2/10 or 20%)

## Document Summary

Probability are always numbers between 0 and 1. 1- means that the event will not happen. Equally likely outcomes- in some situations, all of the possible outcomes of a random experiment occur with the same frequency. Example : when you flip a coin, heads and tails are equally likely; when you roll a die, When dealing with equally likely outcomes, it is sometimes helpful to list all of the. 1,2,3,4,5, and 6 are all equally likely. possible outcome. Sample space - a list that contains all possible (and equally likely) outcomes. Event- any collection of outcomes in the sample space. Represent the sample space with the letter s. Example : the sample space, s , for rolling a die is the numbers, 1,2,3,4,5, and 6. The event get an even number consist of the even outcomes in the sample space, s: 2,4, and 6. Events are represented by uppercase letters: a,b,c, and so on .