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Independent and Dependent Probability

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Independent events - the occurrence of one event has no effect on the probability that a second event will occur. Dependent events, the occurrence of one event does have an effect on the probability that a second event will occur.

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Insert Lesson Title Here Joann flips a coin and gets a head. Then she rolls a 6 on a number cube. independent. Decide whether the set of events are dependent or independent. 1 Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube. independent. Sam chooses a book from the shelf to read, and then Janette chooses a book from the books that remain. dependent. 2 3 4 John draws a card numbered 1–10 and replaces it and draws another card. John draws a card numbered 1–10 and does not replaces it and draws another card. 5 dependent. independent.

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To find the probability that two independent events will happen, multiply the probabilities of the two events. Probability of Two Independent Events = X Probability of both events Probability of first event Probability of second event P(A and B) P(A)P(A)P(A)P(A) P(B)P(B)P(B)P(B)

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An experiment consists of spinning this spinner and rolling a number cube. Find the probability. P(red, 4) = P(yellow, even number) = P(not green, odd number) P(Red or Green, 3 or 2) 1 6 1 4 1 6 1 24 X 1 4 3 6 3 X = 1 8 = 3 4 3 6 9 X = 3 8 = 2 4 2 6 4 X = =

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Thomas roles a number cube 3 times. Find the probability of the following. P(3) = 1/6 = 1/216 P(even) = 1/2= 1/8 Sharon has 4 coins. If Sharon flips all the coins at once, how many outcomes are in the sample space 2=16 1/6 1/2 X X XX XXX 222

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P(Yellow then Blue) = P (Pink then not blue) = P(Yellow then Yellow) = 3 32 == = 2 8 3 8 1 4 3 8 2 8 2 8 1 4 1 4 0 8 5 8 0 64 1 16 = = With Replacing 0 =

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To find the probability that two dependent events will happen, multiply the probability of A and the probability of B after A occurs. Probability of Two Independent Events = Probability of both events Probability of first event Probability of second event after A occurs P(A and B) P(A)P(A)P(A)P(A) P(B following A)

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P(Yellow then Blue) = P (Purple then Purple) = P(Yellow then Yellow) = 3 28 == = 2 8 3 7 1 4 3 7 2 8 1 7 1 4 1 7 1 8 0 7 0 56 1 28 = = With Out Replacing 0 =

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Mary is getting ready to paint her bedroom. Her mother went to the store and purchased samples for her to choose from. Colors# of samples Red shades2 Orange Shades4 Yellow Shades1 Green Shades2 Blue Shades4 Purple Shades3 If she randomly picks a color sample then does not replace it and picks another color sample, then what is the probability of Mary choosing …… A red shade and then a purple shade? A blue shade and then a orange shade? A yellow shade and then a yellow shade? 2 16 3 15 4 16 4 15 1 16 0 15 1 8 1 5 1 4 4 15 = = 1 40 = =0 = 1 1 1 15

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Assignment Page 423 – 424 Problems 1-9 Page 423 – 424 Problems 1-9, 10

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Independent and Dependent Probability Date _____________

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Insert Lesson Title Here Joann flips a coin and gets a head. Then she rolls a 6 on a number cube. Decide whether the set of events are dependent or independent. 1 Kathy draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube. Sam chooses a book from the shelf to read, and then Janette chooses a book from the books that remain. 2 3 4 John draws a card numbered 1–10 and replaces it and draws another card. John draws a card numbered 1–10 and does not replaces it and draws another card. 5

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To find the probability that two independent events will happen, multiply the probabilities of the two events. Probability of Two Independent Events = X Probability of both events Probability of first event Probability of second event P(A and B) P(A)P(A) P(B)P(B)

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An experiment consists of spinning this spinner and rolling a number cube. Find the probability. P(red, 4) P(yellow, even number) P(not green, odd number) P(red or green, 3 or 2)

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Thomas roles a number cube 3 times. Find the probability of the following. P(__) P(______) Sharon has ___ coins. If Sharon flips all the coins at once, how many outcomes are in the sample space

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yb gp br by P(Yellow then Blue) = P (Pink then not blue) = P(Yellow then Yellow) = With Replacing

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To find the probability that two dependent events will happen, multiply the probability of A and the probability of B after A occurs. Probability of Two Independent Events = Probability of both events Probability of first event Probability of second event after A occurs P(A and B) P(A)P(A) P(B following A)

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yb gp br by P(Yellow then Blue) = P (Purple then Purple) = P(Yellow then Yellow) = With Out Replacing

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Mary is getting ready to paint her bedroom. Her mother went to the store and purchased samples for her to choose from. Colors# of samples Red shades Orange Shades Yellow Shades Green Shades Blue Shades Purple Shades If she randomly picks a color sample then does not replace it and picks another color sample, then what is the probability of Mary choosing …… A red shade and then a purple shade? A blue shade and then a orange shade? A yellow shade and then a yellow shade?

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