Post on 29-Dec-2015
“Life is a school of probability” ~ Walter Bagehot
“The only two sure things are death and taxes” ~ cynical philosopher
“Statistically, the probability of any one of us being here is so small that you'd think the mere fact of existing would keep us all in a contented dazzlement of surprise” ~ Lewis Thomas
PROBABILITY
Probability can be defined as the chance of an event occurring
A probability experiment is a chance process that leads to well-defined results called outcomes
An outcome is the result of a single trial of a probability experiment
A sample space is the set of all possible outcomes of a probability experiment
PROBABILITY
Experiment Sample Space
Toss one coin
Roll a die
Answer a true/false question
Toss two coins
EXAMPLES OF SAMPLE SPACE AND PROBABILITY EXPERIMENTS
Find the sample space for the gender of the children if a family has three children. Use B for boy and G for girl.
SAMPLE SPACE
A tree diagram is a device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment
TREE DIAGRAM
An event consists of a set of outcomes of a probability experiment
An event with one outcome is called a simple event
A compound event consists of two or more outcomes or simple events
EVENT
1. Classical or theoretical
2. Empirical or Relative frequency or Experimental
3. Subjective
THE THREE TYPES OF PROBABILITY
Classical probability uses sample spaces to determine the numerical probability that an event will happen. You do not actually perform the experiment to determine the probability.
Classical probability assumes that all outcomes in the sample space are equally likely to occur.
CLASSICAL PROBABILITY
The probability of any event E is the number of outcomes in E divided by the total number of outcomes in the sample space.
Denoted by
FORMULA FOR CLASSICAL PROBABILITY
)(
)()(
Sn
EnEP
What is the probability that the sun will rise tomorrow?
What is the probability that Indiana Jones will come crashing through our window?
What is the probability of getting heads when a coin is flipped?
RANGE OF VALUES FOR PROBABILITY
Probabilities should be expressed as reduced fractions or rounded to two or three decimal places.
When the probability of an event is an extremely small decimal, round to the first nonzero digit after the decimal point.
For example: 0.0000587 would be rounded to 0.00006
ROUNDING RULES
Equally likely events are events that have the same probability of occurring.
For example, flipping a coin and getting heads or tails
EQUALLY LIKELY EVENTS
1. P(3)
2. P(even)
3. P(odd)
4. P(prime)
5. P(4 or 5)
6. P(value less than 7)
FIND THE PROBABILITY OF EACH EVENT USING A SINGLE DIE
1. P(jack)
2. P(heart)
3. P(black ten)
4. P(six of clubs)
5. P(3 or 6)
6. P(3 or diamond)
FIND THE PROBABILITY FOR EACH EVENT USING A STANDARD DECK OF
CARDS