Experimental and Theoretical Probability Essential Question : How can theoretical probabilities be used to predict experimental probabilities?

What is Probability?:

What is Probability? Probability = the likelihood (chance) that an event will occur

Theoretical Probability:

Theoretical Probability Probability can be calculated. There are two types of calculated probabilities: Theoretical Probability Probability based on known information Calculated on the possible outcomes, when they are equally likely Outcomes = the possible results of an event Ex. : When you flip a coin, the possible outcomes are heads and tails.

Example #1: Theoretical Probability:

Example #1: Theoretical Probability Violet rolls a die. What is the probability that she will roll an even number?

Example #1 (cont’d) Thought Process:

Example #1 (cont’d) Thought Process REMEMBER… A die has six possible outcomes. We can roll a 1, 2, 3, 4, 5, or 6. An even number is divisible by two, so on the die, 2, 4, and 6 are even numbers. Thus, the desired outcomes are 2, 4, and 6; they are the numbers that Violet will be happy with if she rolls them. ASK YOURSELF… How many desired outcomes are there? In other words, on the die, how many even numbers (the desired outcome) are there? How many total possible outcomes are there? In other words, on the die, how many numbers are there?

Example #1 (cont’d) Work:

Example #1 (cont’d) Work Using giant ones, we can simplify. is just another way of writing . Answer : The probability that Violet will roll an even number is .

Experimental Probability:

Experimental Probability 2. Experimental Probability Based on data collected from an experiment

Example #2: Experimental Probability:

Example #2: Experimental Probability Mario spins this spinner (the one seen on the right) 20 times. His data is as follows: Blue – 1 Purple – 10 Red – 4 Yellow – 5 Find the probability of spinning yellow.

Example #2 (cont’d) Thought Process:

Example #2 (cont’d) Thought Process ASK YOURSELF… How many successful outcomes are there? In other words, how many times did Mario spin a yellow? How many times did Mario spin his spinner?

Example #2 (cont’d) Work:

Example #2 (cont’d) Work Just like in Example #1, we can simplify using giant ones Answer : The probability that Mario spins a yellow is .

Create a Chart:

Create a Chart Outcomes Tallies Number of Tallies Blue I 1 Purple IIIII IIIII 10 Red IIII 4 Yellow IIIII 5 Outcomes Tallies Number of Tallies Blue I 1 Purple IIIII IIIII 10 Red IIII 4 Yellow IIIII 5 Let’s say that you conduct your own experiment. To stay organized, create a chart like the one below to record your data. Let’s use the data from Example #2.

How can probabilities be represented?:

How can probabilities be represented? Probabilities can be represented as a fraction, decimal, and percent. Refer to Example #2: The answer is . Remember that percents are ratios out of 100 Remember that fractions are the same as division problems Answer : The probability that Mario spins a yellow is or .

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