# 6th Grade - Independent And Dependent Events

 Grade Level: 6th Skill: Statistics Topic: Independent and Dependent Events Goal: Understand the difference between independent and dependent events. Skill Description: Identify independent events and dependent events. Understand that the difference between independent and dependent events is that independent events don’t affect one another, while dependent events do. Know that independent events will always have an unchanging sample space (total number of possible outcomes), while dependent events will have an ever-changing sample space because of the affect of one event on the other. Use the sample space as the denominator of a ratio (fraction) to show a probability of an event, while using the possible favorable outcomes as the numerator (top number). Know how to find the probability of two independent or dependent events by multiplying the probabilities of the separate events. Calculate the probability of two independent events or dependent by multiplying the probabilities of each event.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Identify which events are independent. Explain how you know. A bingo ball is removed from the machine, called out and placed to on the table. A second ball is removed. A bingo ball is removed from a machine, called out and placed back in the machine. A second ball is removed, called out and replaced. (The events in B are independent because the original ball was replaced the player have the same number of chances of their number being picked as they did the first time. The sample space remains the same for all trials.) (2) Identify which events are dependent. Explain how you know. Heidi pulls a card from a deck, records the card number and puts the card in a new pile. She then pulls a second card, records it and places it in the new pile. Heidi pulls a card from a deck, records the card number and replaces the card at the bottom of the deck. She then shuffles the cards and pulls a second card. (The events in A are dependent because the card from event 1 was never replaced. This changed the sample space for event 2.) (3) You are conducting an experiment. There are six cards with the numbers 1 – 6 on each card. What is the probability that you will roll a 4 on your first try and a 6 on your second try? Identify the kind of events described. Explain. (1/36 or about 2.7%, independent events) (4) Tell whether the experiment described below is independent or dependent. Tell how you know. A carnival game has 10 red cups, 25 yellow cups and 15 purple cups. The prizes awarded for red cups are stuffed animals, yellow cups, no prize and purple cups, a poster. You are give two ping pong balls to toss into the cups. (Independent, the first event won’t affect the second event.) (5) Ian has a bag candy with; 5 red, 4 blue, and 1 green. He pulls a candy from the bag records the color than eats it. He then pulls another candy from the bag and repeats these steps. Find P (red, green) (5/90, 1/18, about 5.6%)

### Online Resources

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