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Probability: Experimental Probability Vs. Theoretical Probability

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.

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Probability: Experimental Probability Vs. Theoretical Probability

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  1. Probability: Experimental Probability Vs. Theoretical Probability

  2. 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

  3. 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?

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

  5. 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%

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

  7. 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

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

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

  10. Experimental: 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 How can you tell which is experimental and which is theoretical probability?

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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.) Identifying the Type of Probability

  16. 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.

  17. 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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