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Probability and Simulation

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- The Study of Randomness

- Dontre getting an A on a Precalc quiz
- Richard coming to Precalc class for 5 consecutive days.
- Meha coming to class with starbucks coffee
- Spencer asking Mr. E random questions.

- Experiment: process of measuring or observing an activity for the purpose of collecting data. Ex: rolling a pair of dice
- Outcome: A particular result of an experiment. Ex: rolling a pair of threes with the dice.
- Sample Space: All possible outcomes in an experiment. Ex: sample space of a die {1, 2, 3, 4, 5, 6}
- Event: One or more outcomes that are of interests for the experiment. Ex: rolling a total of 2, 3, 4, or 5 with 2 dice

- Suppose that you roll a die once. There will be 6 possible outcomes; you may get either 1, 2, 3, 4, 5 or 6. These possible outcomes of such a random experiment are called the basic outcomes. The set of all basic outcomes is called the sample space. The symbol S will be used to denote the sample space.

S = sample space

- What is the sample space for a roll of a single six-sided die?

S = {1, 2, 3, 4, 5, 6}

What is the sample space for a tossing a coin?

S = { T, H}

Number of possible outcomes in which EVENT A occurs

P[A]=

Number of possible outcomes in the SAMPLE SPACE

Refers to the situation when we know the number of possible outcomes of the event of interest and can calculate the probability of that event.

Event A = rolling a total of 2, 3, 4, or 5

P[A]=?

A = 10

P[A]= 10/36

= 0.28

S = 36

Classwork

Find the Probability of the following events

A = same number

17%

25%

B = both odd number

50%

C = sum of 7, 8, 9, or 10

50%

D = an odd and an even number

50%

E = not getting a sum of even number