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Solve for x. 28 = 4(2x + 1) + 4 28 = 8x + 4 + 4 28 = 8x + 8 – 8 – 8 20 = 8x 8 8 2.5 = x Distribute Combine Subtract Divide

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PSD 305: Use the relationship between the probability of an event and the probability of its complement PSD 403: Determine the probability of a simple event PSD 402: Translate from one representation of data to another (e.g., a bar graph to a circle graph PSD 404: Exhibit knowledge of simple counting techniques*

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Probability is the study of random events. The probability, or chance, that an event will happen can be described by a number between 0 and 1: A probability of 0, or 0%, means the event has no chance of happening. A probability of 1/2, or 50%, means the event is just as likely to happen as not to happen. A probability of 1, or 100%, means the event is certain to happen.

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You can represent the probability of an event by marking it on a number line like this one Impossible 0 = 0% 50 – 50 Chance ½,.5, 50% Certain 1 = 100% The language of probability includes: Experiment – an investigation where the answer is unknown Trial – one specific instance of an experiment Outcome - the result of a single trial Event – a selected outcome, such as getting an 11 from rolling two dice Event Space/or Sample Space – the set of all possible outcomes of an experiment

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When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to rain. If the chance drops to 20%, then it may rain, but it probably will not rain.

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Event – This is the selected outcome. Ex. If event A is the probability of rolling a 5 or higher, the probability is 2/7, so P(A) = 2/7. Complement – This is the probability of everything other than the event. Ex. In the example above, the complement is rolling 4 or lower, so the complement of event A is 5/7, or P(A) = 5/7. Probability of “A Bar”

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If you toss a coin twice, what are the possible outcomes? HH, TT, HT, TH What is the probability of two heads? HH, TT, HT, TH = What is the probability of at least one head? HH, TT, HT, TH = It’s complement would be 3/4! It’s complement would be 1/4! 1/4 3/4

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-Find a partner to play. -To play this game, you need an ordinary six-sided die. -Each turn of the game consists of one or more rolls of the die. -You keep rolling until you decide to stop or until you roll 1. -You may choose to stop rolling at any time.

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Scoring: If you choose to stop rolling before you roll 1, your score for that turn is the sum of all the numbers you rolled on that turn. However, if you roll 1, your turn is over, and your score for that turn is 0.

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Ex. 1: you roll 4, 5, and 2 and then decide to stop. Your score for this turn is 11. Ex. 2: You roll 3, 4, 6, and 1. The turn is over because you rolled 1, and your score for this turn is 0. Each turn is scored separately. Add up all your points to determine the winner. Each player will have 10 turns.

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You will play a total of 3 games against 3 different people!

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Questions: 1. How did you decide whether or not to roll again? 2. What strategies did you try? Which worked best for you? 3. If you were playing for a prize, would your strategy change?

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Probability What are your Chances? Overview Probability is the study of random events. The probability, or chance, that an event will happen can be described.

Probability What are your Chances? Overview Probability is the study of random events. The probability, or chance, that an event will happen can be described.

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