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Understanding Probability: Independent Events and Coin Tosses

This resource explores the fundamentals of probability, focusing on independent events, zoals coin tosses. We will start by examining single coin flips, calculating the probability of landing on Tails. Next, we delve into more complex scenarios, including flipping a coin three times and determining the probabilities of obtaining two Heads and one Tail. With the aid of tree diagrams, we simplify the process of counting outcomes and understanding independence between events. Practice problems are available to help solidify these concepts.

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Understanding Probability: Independent Events and Coin Tosses

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  1. Probability D2 Independent Events

  2. Two or More Independent Events 1 WW Question 1 – What is the probability of tossing a coin and getting Tails? E 2

  3. Two or More Independent Events • Question 2 – What is the probability of tossing a coin 3 times and getting 2 Heads and a Tail? How do we figure this out? First, we need a starting point Start with a tree diagram Coin 1 – what are the possible outcomes? Coin 2 – what are the possible outcomes? Coin 3 – what are the possible outcomes? Heads or Tails H T H T H T H T H T H T H T Now we have to check each branch Remember, we only count the last row 3 WW Is that what we want? Yes No E 8 Do I have2 Heads and 1 Tail?

  4. Two or More Independent Events Independent Events: The outcome of one event _______ ______ affect the outcome of another event • does • NOT It does not matter if you get a Head or Tails the first time you toss a coin The chances of getting Tails the second time is still 50/50 So what happens the first time does NOT affect what will happen the second time

  5. Two or More Independent Events Independent Events: The outcome of one event _______ ______ affect the outcome of another event • does • NOT • Draw a tree diagram • Count ONLY the last row • Use the WWE formula

  6. Examples of Independent Events A. Brianna is using the two spinners shown to play her new board game. She spins the arrow on each spinner once. Find the probability that Brianna will move fewer than four spaces and backward 1 2 3 4 • Draw a tree diagram F B F B F B F B • Count ONLY the last row 3 • Use the WWE Formula ? • What do we want? WW E 8 • Over everything • How many total?

  7. Examples of Independent Events B. A die is rolled and a coin is tossed. What is the probability of getting an odd number and tails? • Draw a tree diagram 1 2 3 4 5 6 H T H T H T H T H T H T 3 WW • What do we want? • Over everything E 12 • How many? • Count ONLY the last row

  8. In Closing • What is different between single event and independent events?

  9. Practice Problems • Now try the practice problems on your own • Notice that you MUST draw a tree diagram for each problem

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