# Experimental Probability vs Theoretical Probability Experimental vs Theoretical

Experimental Probability vs. Theoretical Probability

Experimental vs. Theoretical Experimental probability: when you do the experiment. P(event) = number of times event occurs total number of trials Theoretical probability: what should happen in an ideal situation. P(E) = number of favorable outcome total number of possible outcomes

How can you tell which is experimental and which is theoretical probability? • •

Identifying the Type of Probability •

Identifying the Type of Probability •

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

The imitation of chance behavior based on a model that accurately reflects the experiment under consideration, is called a simulation. We can estimate probabilities by performing a simulation through the use of an experimental model. Some of our simulations can be done quite easily using actual probability tools like dice or spinners. Some situations, though, will require us to use a random number generator or a table of random digits.

Steps for Conducting a Simulation 1. 2. 3. 4. 5. State the problem or describe the experiment State the assumptions Determine how to represent outcomes Simulate many repetitions State your conclusions

Step 1: State the problem or describe the experiment Mr. and Mrs. Worthalot plan to have 5 children. Mr. Worthalot really wants to have all boys; Mrs. Worthalot wants to have all girls. What is the probability that the couple will have all girls or all boys? We can’t ask Mrs. Worthalot to have 5 children over and over again, so we simulate the experiment.

Step 2: State the Assumptions • There are two assumptions here: • A boy or girl is equally likely to occur on each pregnancy • Each baby’s gender is independent of each other – the first baby’s gender will not have an effect on the gender of any subsequent baby

Step 3: Determine how to represent the outcomes Since there are two, equally likely outcomes, we have a lot of options: • Flip a coin: heads is boy, tails is girl • Roll a die: evens are boy, odds are girl • Pick a card: black cards are boy, red cards are girl (must replace cards each time) • Use a random number generator on the calculator and let 0 = boy and 1 = girl.

Step 4 Simulate many repetitions To run the simulation in real life, we would repeat it hundreds of times… you won’t have to do that! But we should repeat it many times. Let’s use a coin. We would flip the coin five times, over and over again, and record how many times we got 5 heads or 5 tails.

Your chart might look like this: TRIAL 1 2 3 4 5 6 7 8 9 10 HEADS 3 4 0 1 4 2 1 2 3 1 TAILS 2 1 5 4 1 3 4 3 2 4

Step 5 – State your conclusions. We estimate the probability of a run by the proportion. Let’s say we ran the simulation 50 times and 5 children of the same gender came up 3 times, the experimental probability would be 3/50, or 0. 06.

Let’s Try One! 75% of all high school seniors have a job. What’s the probability that, in a group of 8 seniors, at least 5 of them are employed? Set up a simulation are run it 20 times.

- Slides: 15