Aim: How do we find the probability of a simple event?

Complete Worksheet

Basic Concepts• Probability: the chance of an event occurring • Probability Experiment: is the chance process

that leads to well-defined results called outcomes.

• Outcomes: is the result of a single trial of probability experiments

• Sample Space: the set of all possible outcomes of a probability experiment

• Event: consists of a set of outcomes of a probability experiment

Finding Sample Spaces of Multiple Trials

• Tree Diagram: a device consisting of line segments emanating from a starting point and also form the outcome point. It is used to determine all possible outcomes of a probability experiment

What is an event?

• Event: consists of a set of outcomes of a probability experiment

• The event can be one outcome or ore than one outcome– Example: if a die is rolled and a 6 shows, this result

is called an outcome

Simple VS Compound Event

• An event with a single trial/one outcome is called a simple event

• An event consisting of two outcomes/simple events or more is called a compound event

Classic Probability

• Classical Probability: uses sample spaces to determine the numerical probability that an event will happen.

• The experiment does not have to occur in order to find the probability

• Classical Probability assumes that all outcomes in the sample space are equally likely to occur. – Equally likely events are events that have the same

probability of occuring

Formula for Classical Probability

• The probability of any event E is number of outcomes in E .

Total number of outcomes in S

• This probability is denoted by P(E) = n(E)

n(S)• This probability is called classical probability and

it uses the sample space S

How do we express probability?

• Probability can be expressed as a fraction, decimal or when appropriate a percentage

Rounding Rules for Probability

• Probability should be expressed as reduced fractions or rounded to two or three decimal place

• When the probability of an event is an extremely small decimal, it is permissible to found the decimal to the first nonzero digit after the point– Example: 0.0000587 would be .00006

Quiz

1. What is a probability experiment?2. Define sample space3. What is the difference between an outcome and

an event?4. What are equally likely events?5. What is the range of values of the probability of

an event?6. When an event is certain to occur, what is the

probability?

Class Work

1. Find the sample space for the gender of the children in a family having three children. Use B for Boy and G for Girl. Use a tree diagram to find the same space for the gender of three children in the family.

2. For a card drawn from an ordinary deck, find the probability of getting a queen.

3. If a family has three children, find the probability that all the children are girls.

Class Work Solutions

1. S = {BBG, BBB, BGB, GGG, GGB, GBB, GBG, BGG}

2. 1/133. 1/8