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Mrs Patek has three pairs of capri pants, a black pair, a tan pair and a blue pair. She also has two different T- shirts, one white and one pink. Make a tree diagram to show all the possible outfits. Counting Principle What is the probability you will select the black capri pant and the pink T- shirt when selecting an outfit at random?

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Lindsey flips a coin and rolls a number cube at the same time. Draw a tree diagram to display the possible choices. What is the probability you will get a heads and an even number?

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1.) How many possible outcomes are there for flipping a coin three times? 2.) P(exactly two heads)3.) P(one head) 4.) P(three tails)5.) P(at least two tails) Draw a tree diagram to show all the possible outcomes for flipping a coin three times.

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Critical Thinking: What's the shortcut for finding the total number of possible choices? Answer: Multiply the number of choices from each category. This shortcut is called the Counting Principle or Multiplication principle 2 6 = 12 choices coin # cube

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Examples of the Counting Principle: 1.) Jordan has a choice of wheat bread or rye bread and a choice of turkey, ham, or tuna for lunch. How many possible sandwich choices are there? bread lunch meat = 2.) Jimmy is buying a new car and has a different choices as to the options. There are, 6 different exterior colors 2 interior colors 4-cylinder, 6-cylinder, or 8-cylinder engine single CD or 6-CD player How many different cars does Jimmy have to chose from? =

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Using the Counting Principle to find Probability A combination lock has 20 numbers on its dial. To open the lock, you must have the correct three number combination. What is the probability that you randomly select the correct combination to a lock, if you select three numbers at random? 1.) Use the counting principle to find the number of possible combinations. 2.) Write the probability that you will select the correct combination?

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A B C D E F H G Use the multiplication principle to find the total number of possible outcomes. Then determine the probability of the event. 1.) You spin spinner X two times. Find the probability of spinning a C, then a B. Spinner X Spinner Y 2.) You spin spinner y two times. Find the probability of spinning an A, then a B. 3.) You spin spinner X and then spinner Y. Find the probability of spinning a G, then a B. A B

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1.) An Italian restaurant offers small, medium and large calzones. The choices of fillings are cheese, sausage, spinach or vegetable. How many different calzones can you order? 2.) There are four different flavors of ice-cream at Lynn’s Luscious Ice Cream shop (vanilla, chocolate, strawberry and chocolate-chip). There are three different types of sauce (caramel, chocolate and strawberry) How many different types of sundaes are possible? Demonstrate Understanding:

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3.) Make a tree diagram to show the sample space for tossing a coin and spinning a spinner with five equal sections that are numbered 1-5. 4.) P(heads, 2) 5.) P(tails, odd)

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When dealing with the occurrence of more than one event, it is important to be able to quickly determine how many possible outcomes exist. http://regentsprep.org/Regents/Math/counting/Lcount.htm.

When dealing with the occurrence of more than one event, it is important to be able to quickly determine how many possible outcomes exist. http://regentsprep.org/Regents/Math/counting/Lcount.htm.

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