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Published byToby Fowler Modified over 6 years ago

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What is Probability? The study of probability helps us figure out the likelihood of something happening. In math we call this “something happening” or an “event” Probability is a way of expressing what the chances are that an event will occur

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The term probability is common Weather forecast - 30 % chance of rain Gambling - two dice will produce a sum of 7 is 1/6 Things to know: 1 st thing: What the probability statements mean 2 nd thing: Then we consider how we determine the numerical value for that probability

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Probability Problems Problem: A spinner has 4 equal sectors colored yellow, blue, green, and red. What are the chances of landing on yellow after spinning the spinner? Solution: The chances of landing on yellow are 1 in 4, or one fourth.

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Probability Problems Very important to identify all of the different outcomes that could occur Outcomes = the different results that could happen in the event or the different possibilities To find a basic probability with all outcomes equally likely, we use a fraction: number of favorable outcomes total number of possible outcomes Probability =

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What is a favorable outcome? Example: A spinner has 4 equal sectors colored yellow, blue, green and red. Want to find the probability of the spinner landing on yellow. Favorable outcome =landing on yellow section The probability of landing on yellow is 1 in 4 or 1/4

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Experiment: A spinner has 4 equal sectors colored yellow, blue, green and red. After spinning the spinner, what is the probability of landing on each color? Possible Outcomes: The possible outcomes of this experiment are yellow, blue, green, and red. P(yellow) = number of ways to land on yellow = 1 total number of colors 4 P(blue) = number of ways to land on blue = 1 total number of colors 4 P(green) = number of ways to land on green = 1 total number of colors 4 P(red) = number of ways to land on red = 1 total number of colors 4 Probabilities:

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Example: Number of ways 2 dice would produce a sum of 7 Die 1 Die 2 Die 1 Die 2 Die 1 Die 2 Die 1 Die 2 Die 1 Die 2 Die 1 Die 2 112131415161 122232425262 132333435363 142434445464 152535455565 162636465666

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36 different combinations Shows all the different ways the dice can land Shows all the ways you could roll a seven 6 of the 36 produce the sum of 7 Must assume that each of the 36 combinations are equally likely to occur So there is a 1/6 chance that you the sum of the dice will be 7

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What is the total number of possible outcomes? Is called a sample space Sample space is a set consisting of all the possible outcomes of an event. The number of different ways you can choose something from the sample space is the total number of possible outcomes.

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Example: Jar with 4 red marbles and 6 blue marbles Want to find the probability of drawing a red marble at random. Favorable outcome = drawing a red marble

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So we have 4 red marbles and 6 blue marbles in our jar Sample space = all ten marbles because we are likely to draw any one of them Favorable outcomes = # of red marbles = 4 Possible outcomes = total # of marbles = 10 4/10 reduces to 2/5 Probability of drawing a red marble where all outcomes are equally likely is 2/5 (sample space)

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Ways to Express Probability As a fraction~ 4/10 = 2/5 As a decimal ~ 4/10 =.4 As a percent ~ 4/10 = 40/100 = 40% Unlikely events have a probability near zero Likely events have probabilities near 1

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Probability is a fraction of the sample space The sum of the probabilities of all the possible outcomes equals 1 The probability of the occurrence of an event is always 1 minus the probability that it doesn’t occur

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P(yellow) = number of ways to land on yellow = 1 total number of colors 4 P(blue) = number of ways to land on blue = 1 total number of colors 4 P(green) = number of ways to land on green = 1 total number of colors 4 P(red) = number of ways to land on red = 1 total number of colors 4 Probability = ¼ Sample space = 4 colors Sum = ¼ + ¼ + ¼ + ¼ = 1 Probability of NOT landing on yellow = 1-1/4 = 3/4 Spinner problem

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Marble Problem Probability of picking a red marble was 4/10 or 2/5 Sample space = 10 marbles in the jar So the probability of not picking a red marble 1 = 10/10 10/10 -4/10 = 6/10 or 3/5 (this is also the probability of picking a blue marble)

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We only have 2 events with our red and blue marbles Either we pick a red marble or a blue marble If you don’t do the first, then you must do the second So the probability of picking a red marble plus the probability of picking a blue marble equals 1 or 100% Sum = 4/10 + 6/10 = 10/10 = 1

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Situation with 2 events You draw 1 marble from the 10 Then I draw another marble from the nine that remain What is the probability that I will draw a blue one first? What is the probability that you will draw a red one second?

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Your probability of drawing a blue one is 6/10 After you draw there are only 9 marbles left and 4 of those are red, so the probability that I will draw a red one is 4/9 When there are 2 events, the second outcome is dependent on the first.

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What can you learn from the chart? Classroom Exercise/Homework

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%’s of colors in different kinds of M & M’s 1/2007

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