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Dependent Events

Dependent Events. Depend ent Event. What happens during the second event depends upon what happened before. In other words , the result of the second event will change because of what happened first.

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Dependent Events

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  1. Dependent Events

  2. Dependent Event • What happens during the second event depends upon what happened before. • In other words, the result of the second event will change because of what happened first. The probability of two dependent events, A and B, is equal to the probability of event A times the probability of event B. However, the probability of event B now depends on event A.

  3. Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get 2 black pens? P(black first) = P(black second) = (There are 13 pens left and 5 are black) THEREFORE……………………………………………… P(black, black) =

  4. Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get: P(blue first) = P(black second) = P(blue, black) =

  5. Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get: P(blue first) = P(blue second) = P(blue, blue) =

  6. Tossing two dice and getting a 6 on both of them. • 2. You have a bag of marbles: 3 blue, 5 white, and 12 red. You choose one marble out of the bag, look at it then put it back. Then you choose another marble. • 3. You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back. • 4. You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another tile. TEST YOURSELF Are these dependent or independent events?

  7. Probability of Dependent Events • A basket contains 6 apples, 5 bananas, 4 oranges, and 5 peaches. Leslie randomly chooses one piece of fruit, eats it, then chooses another. What is the probability that she chose a banana and then an apple?

  8. Dependent Events Find the probability • P(Q, Q) • All the letters of the alphabet are in the bag 1 time • Do not replace the letter x = 0

  9. Probability of Three Dependent Events • You and two friends go to a restaurant and order a sandwich. The menu has 10 types of sandwiches and each of you is equally likely to order any type. What is the probability that each of you orders a different type?

  10. There are 20 dogs at the dog park. 3 are brown, 9 are black, 6 are white, and 2 are yellow. You will not replace each dog before the next selection. P(white, black)

  11. There are 20 dogs at the dog park. 3 are brown, 9 are black, 6 are white, and 2 are yellow. You will not replace each dog before the next selection. P(yellow, yellow)

  12. The Fundamental Counting Principle Mr. Swaner

  13. Using a Tree Diagram • You can use pictures in a diagram to represent a situation: • For a trip you pack 3 shirts and 4 pairs of shorts. How many different outfits can be made?

  14. For a trip you pack 3 shirts and 4 pairs of shorts. How many different outfits can be made?

  15. You Try • A restaurant serves hamburgers and veggie burgers. The condiments choices are: lettuce, tomato, pickle, onion, and cheese. How many different ways can the burger be made if you can only have one condiment?

  16. hamburger veggie burger

  17. Sometimes making a tree diagram just doesn’t make sense. • You should have noticed that you could just multiply the numbers together

  18. The Fundamental Counting Principle • If there are m ways to choose the first item and n ways to choose the second item, the number of possible item choices are: You multiply the number of each possibility together to find the total possibilities.

  19. Example • You go to Subway for lunch. There are 4 types of bread, 3 types of meat, and 3 different sizes. How many different sandwiches could you have? • Instead of drawing a tree diagram, you can use the fundamental counting principle.

  20. Try One • You are ordering a one topping pizza. You can have pepperoni, olives, sausage, onions, or peppers. You could also order a small, medium, or large. There are also different types of crusts: thin, deep dish, and stuffed. • How many different types of pizza could you order?

  21. Try One • A store sells t-shirts in small, medium, large, and extra large. They come in red, green, black, and blue. • How many different t-shirts are there? • If you picked one at random, what is the probability it will be red and medium?

  22. Closure – with a partner • You randomly select two cards from a standard 52-card deck. What is the probability that the first card is not a face card (a king, queen, or jack) and the second card is a face card if: • (a) you replace the first card before selecting the second, and • (b) you do not replace the first card?

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