# Probability Experimental Probability Vs Theoretical Probability What do

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 in 6 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? Experimental: Theoretical: You tossed a coin 10 Toss a coin and times and recorded getting a tail or a a head 3 times, a tail head is 1/2. 7 times P(head) = 1/2 P(head)= 3/10 P(tail) = 1/2 P(tail) = 7/10

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 HEADS TAILS 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.

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 ü 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 ü 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 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

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