Probability: Experimental Probability Vs. Theoretical Probability

What do you know about probability? Probability is a number from 0 to 1 that tells you how likely something is to happen. Probability can have two approaches -experimental probability -theoretical probability

Life is a series of Probabilities There is a 30% chance of rain. Do I go to the beach? Should I buy the extended warrantee on my new Macbook? Do I leave my house an hour before my flight out of Logan, or two hours before? Should I buy health/life/disability insurance?

Probability Example What is the probability of rolling a 5 on a fair, 6-sided die? How do I express the probability?

Probability Review What is the probability of rolling a 5 on a fair, 6-sided die? 1 in 6 How do I express the probability? 1/6 0.167 16.7%

Tree Diagram A tree diagram shows all possible outcomes of an event by linking each set of combinations through “branches” (example on next slide)

Example of Tree Diagram If a coin is tossed and a single di is rolled simultaneously, then the probability of getting heads on a coin and the number 4 on the di is 1/12

Contrast experimental and theoretical probability Experimental probability is the result of an experiment. Theoretical probability is what is expected to happen.

Experimental vs.Theoretical Experimental probability: P(event) = number of times event occurs total number of trials Theoretical probability: P(E) = number of favorable outcomes total number of possible outcomes

How can you tell which is experimental and which is theoretical probability? You tossed a coin 10 times and recorded a head 3 times, a tail 7 times P(head)= 3/10 P(tail) = 7/10 Theoretical: Toss a coin and getting a tail or a head is 1/2. P(head) = 1/2 P(tail) = 1/2

Experimental probability Experimental probability is found by repeating an experiment and observing the outcomes. P(heads)= 3/10 A head shows up 3 times out of 10 trials, P(tails) = 7/10 A tail shows up 7 times out of 10 trials

Theoretical probability P(heads) = 1/2 P(tails) = 1/2 Since there are only two outcomes, you have 50/50 chance to get heads or a tails. HEADS TAILS

Compare experimental and theoretical probability Both probabilities are ratios that compare the number of favorable outcomes to the total number of possible outcomes P(heads)= 3/10 P(tails) = 7/10 P(heads) = 1/2 P(tails) = 1/2

Identifying the Type of Probability A bag contains 4 red marbles and three blue marbles. P(red) = 4/7 Theoretical (The result is based on the possible outcomes)

Identifying the Type of Probability You draw a marble out of the bag, record the color, and replace the marble. After 6 draws, you record 2 red marbles P(red)= 2/6 = 1/3 Experimental (The result is found by repeating an experiment.)

Law of the Large Numbers 101 This Law states that as the number of trials increase, the experimental probability will get closer and closer to the theoretical probability.

Lesson Review Probability as a measure of likelihood There are two types of probability: Theoretical--- theoretical measurement and can be found without experiment Experimental--- measurement of a actual experiment and can be found by recording experiment outcomes

Homework Page 17, #1, 4 Page 18, #9 Page 20, #19 Page 21, #21-23