1. = Basic Probability Notes Basics of Probability Probability
Definitions
Experiment – activity under consideration
Outcomes – observable results from the experiment
Trials – repetition of the experiment
Relative frequency – this is the probability of a certain outcome (like temperature, or an exam grade)
Experimental Probability ­ The probability of what happens during trials
Theoretical Probability ­ The probability of what should happen during trials
Basics of Probability
Sample Space – all your possible outcomes What is your sample space for the following:
flipping a coin once
flipping a coin twice
rolling a die
rolling 2 dice
Event – subset of your sample space Example: rolling a 3 with one die,
flipping a coin and getting heads
Probability
How to find probability:
# of ways an event can occur
Total number of outcomes
Experimental Probability
Probability =
Theoretical =
# times an event occurs
Total number of trials
Example
A college has an enrollment of 1210 students. The number in each class is as shown.
Class # of students
Example
Allen has a bucket of chips. In this bucket there are 5 red, 6 yellow and 2 black chips. Find each probability.
P(red)
P(white)
P(not black)
Freshmen
420
Sophomore
315
Junior
260
Senior
215
Total
1210
What is the probability that a student selected at random will be a
Freshman? Sophomore? Junior? Senior?

2. Experimental is not always the same as theoretical.
Basic Probability Notes
Example
Sample space for a standard deck of cards
A card is randomly selected from a standard deck of cards. Find each probability.
P(Face Card)
P(red seven)
P(heart)
EX: Flipping a coin
What is the probability of it landing on heads?
What if you flipped the coin 3 times? How many possible out comes are there?
Example
Sample space for rolling a pair of dice
A pair of dice is rolled. Find each probability.
P( both die are even)
P(sum is 10)
P(roll doubles)
P(sum is 13)
P(sum is > 2)
Rules of Probability
P(A) is always between 0 and 1
If P(A)=0, then P(B) is 100
If P(B)=0 then P(A) IS 100
Theoretical vs. Experimental Probability
Theoretical Probability:
Experimental (Empirical) Probability:
Theoretical vs. Experimental Probability continued: Law of Large Numbers
Experimental is not always the same as theoretical.
After a large number of trials, experimental probability should get closer to the theoretical probability.