Transcript lesson10-probability of simple events

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 space
3. 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. 1/13
3. 1/8