Homework Questions

Simulations Unit 6

Experimental Estimates As the number of trials in an experiment increases, the relative frequency of an outcome approaches the probability of the outcome.

Example 1 (review) An experiment consists of throwing a dart at a target. Suppose the experiment is repeated 200 times, with the following results: yellow 43, red 86, blue 71 Write the probability distribution for the experiment

Probability Simulations In order to estimate probability using the experimental approach, a large number of trials is needed. Instead of actually carrying out the experiments, computer simulators are used…aka your calculator!

Random Number Generator On your calc: Math Prob 5: RandInt(

Example 2 Use your calc to create a probability distribution for the experiment of tossing 3 coins and counting the number of heads. Assign 0=heads, 1-tails RandInt(0, 1, 3) Repeat 10 times OutcomeFrequencyProb. 0 heads 1 heads 2 heads 3 heads

Experimental v. Theoretical Experimental Probabilities are what happens when you carry out the experiment. Theoretical probabilities are used when outcome are equally likely. Rolling a dice = 1/6 chance each time

Example 3 Use properties of probability to write a theoretical probability distribution for the experiment in #2. How do these compare to #2? OutcomeOptionsProb. 0 heads 1 heads 2 heads 3 heads

Counting Techniques A catalog offers chairs in a choice of 2 heights, regular and tall. There are 10 colors available for the finish, and 12 choices of fabric for the seats. The chair also has 4 different possible designs. How many different chairs can be ordered?

Example 5 Each letter of the alphabet is written on a piece of paper, and three letters are chosen at random. There are two important questions to ask: Is each letter replaced before the next letter is chosen? Does the order of the letters matter in the result?

With replacement – the number to chose from stays the same Without replacement – the number to chose from decreases by one each time Order important – CAT is different than ACT Any order – CAT, CTA, TAC, TCA, ACT, and ATC are considered the same

3 letters are chosen… With replacement, order important Without replacement, order important Without replacement, any order

Homework Worksheet (1-25)