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Bell Work: Factor x – 6x – 16 2

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Answer: (x – 8)(x + 2)

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Lesson 70: Probability and Designated Order

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The study of probability began when people began studying games of chance such as flipping coins, rolling dice, drawing cards from a deck, or drawing marbles from an urn. Problems from games of chance still provide the best models on which to base a study of elementary probability, and we will concentrate on these problems.

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The study of probability is based on the study of outcomes that have an equal chance of occurring.

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It is customary to call activities such as flipping coins, rolling dice, blindly selecting cards from a deck, and drawing marbles from an urn experiments and to call the individual results outcomes.

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We call the set of equally probable outcomes the sample space for the experiment. A toss of a fair coin has two equally probable outcomes. Thus, the sample space for a coin toss is heads or tails, as shown below. HT

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The roll of a single die has six equally probable outcomes. Thus, the figure below shows the sample space for the roll of a single die. 123456

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We define the probability of a particular even as the number of outcomes that satisfy the requirement divided by the total number of outcomes in the sample space. particular event=number outcomes that satisfy requirement total number of outcomes in sample space

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The probability of any event is a number between 0 and 1 inclusive. If no outcomes satisfy the requirement, the probability is 0, and if every outcome satisfies the requirement, the probability is 1.

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Thus we see that a probability of - 2 of 7 ½ is not possible because the probability of any event must be a number between 0 and 1.

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Example: A fair coin is tossed three times and comes up heads every time. What is the probability that on the next toss it will come up heads?

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Answer: P = number of outcomes outcomes in sample space P = ½

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Example: Six green marbles and eight red marbles are placed in an urn. One marble is drawn and then dropped back in the urn. Then a second marble is drawn and dropped back into the urn. Both marbles were red. If another marble is drawn, what is the probability that it will be red?

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Answer: P = 8/14 = 4/7

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Practice: A single die is rolled three times. The results are 1, 4, and 3, in that order. What is the probability that the next roll will produce a number greater than 2?

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Answer: 4/6 = 2/3

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Practice: Two dice are rolled. What is the probability that the sum of the numbers rolled is 7 A number greater than 8

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Answer: 6/36 = 1/6 10/36 = 5/18

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Designated Order: The probability of future outcomes of independent events happening in a designated order is the product of the probability of the individual outcomes.

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For example, if we toss a coin twice, the probability of getting a heads on the first toss and a tails on the second toss is one fourth. P(H, T) = P(H) x P(T) = ½ x ½ = ¼

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Example: A fair coin is tossed four times. What is the probability that the first two times it comes up heads and the last two times it comes up tails?

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Answer: ½ x ½ x ½ x ½ = 1/16

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Practice: The spinner show is spun twice. What is the probability that the spinner stops on 4 and then on 3?

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Answer: ¼ x ¼ = 1/16

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HW: Lesson 70 #1-30

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