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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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Presentation on theme: "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."— Presentation transcript:

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

2 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*

3  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.

4 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

5  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.

6 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”

7  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

8 -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.

9  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.

10  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.

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

12 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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