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Probability

Probability. D3 Dependent Events. Two or More Dependent Events. Question – A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. John randomly draws a marble then Noah also selects a marble. What is the probability that they will both be red?. WW. E. John. Noah. 4. 4?. 3.

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Probability

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  1. Probability D3 Dependent Events

  2. Two or More Dependent Events Question – A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. John randomly draws a marble then Noah also selects a marble. What is the probability that they will both be red? WW E • John • Noah 4 4? 3 12 • = 12 12? 11 132 But didn’t John take one of the red ones? How many marbles are left? So what are Noah’s chances of getting a red one? Now we multiply them

  3. Two or More Independent Events Dependent Events: The outcome of one event ______ affect the outcome of another event • DOES When John took a red marble, it affected Noah’s chances of getting one as well • 1. Find the probability of the first event • 2. Find the probability of the second event (and third, and fourth, etc) • 3. Multiply them

  4. Examples of Dependent Events With and Without Replacement A. Two cards are drawn from a deck with replacement (This means that one person chooses a card, looks at it and returns it, and then another person chooses a card, looks at it, and returns it.) What is the probability that the first card is an Ace and the second card is black? 4 26 104 WW • = E 52 52 2704 • Over everything • What do we want? • How many Aces are there? • How many black cards are there? • How many cards total are there? • So the 2 black Aces are still in the deck

  5. Examples of Dependent Events With and Without Replacement B. Two cards are drawn from a deck without replacement. What is the probability that the both of the cards are black? 26 25 26? 650 WW • = E 52 52? 51 2652 • What do we want? • How many black cards are there? • But we already used one • Over everything • How many cards are there total? • But we already used one

  6. Examples of Dependent Events With and Without Replacement 3 C. A bag contains 4 red marbles, 3 white marbles, and 6 blue marbles. What is the probability of randomly selecting a red marble, setting it aside, and then randomly selecting a white marble from the bag? 4 3 12 WW • = E 13 13? 12 156 • Over everything • No. We took one of the red ones away

  7. Examples of Dependent Events With and Without Replacement D. A bag contains 4 red marbles, 3 white marbles, and 6 blue marbles. What is the probability of randomly selecting a red marble, replacing it, and then randomly selecting a white marble from the bag? 4 3 12 WW • = E 13 13 169 • Over everything • How many marbles total?

  8. In Closing • What is the difference between independent and dependent events?

  9. Practice Problems • Now try the practice problems on your own

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