ProbabilityExperiments

Problem SolvingSample Spaces

Theoretical vs ExperimentalCompound Events

Independent and Dependent Events

Experimental Probability• P(E) =

• Lets say you flipped a coin 10 times. You got 6 heads and 4 tails.• What is the probability, based on your experiment, that you flip a

head next time?

• What is the theoretical probability that you will get a head next time?

Experimental Probability (Cont.)Political Party RespondentsDemocrat 246

Republican 175

Moderate 43

Independent 36

What is the probability that someone will vote for a Democrat?

Is this the theoretical probability or experimental probability?

Do you suspect the theoretical and experimental probability are similar?

Sample Spaces and Theoretical Probability• Theoretical Probability is similar to experimental probability in that it

is favorable/total for its formula. The difference is that rather than using data collected from an experiment or a survey, we use logic and reasoning to determine the probability.

• Example, you could flip a coin and get a result other than 5 heads and 5 tails, but theoretically, your next coin toss should be 50% heads and 50% tails.

Compound Events• The probability of A and B occurring. P(A) * P(B).• Remember, Probability is between 0 and 1

• Example. What is the probability of flipping a coin head and rolling a 6 on a die• Flipping a coin is .5 and rolling a die to get a 6 is .1666• Is the chance of doing both great then doing either? Less than doing either?

• How do we get to such a result?

Independent Events/Dependent Events• Independent Events. When one event has no consequence over

another event.• P (B and A) = P(A)*P(B)

• Dependent Events. When one event alters the results of the other event.• P(B and A) = P(A)*P(B given that A occurred)• Example: What is the probability of drawing two queens from a deck of

cards?