Related Topics:
More Lessons for Grade 6
Math Worksheets
Examples, solutions, videos, worksheets, stories, and songs to help Grade 6 students learn about independent and dependent events in probability.
Independent vs Dependent Events
Understanding the difference between Independent and Dependent events.
Example:
Given a
bag of 10 marbles where 2 of the marbles are black, what is the probability of pulling a black marble two times in a row?
a) if you put the first marble back in the bag. (Independent Events)
b) if you keep the first marble. (Dependent Events)
Probability-Independent
and Dependent Events
Independent events are when two or more events have no effect on the occurrence of each other.
Dependent events are when the occurrence of one event has an effect on the other.
Examples:
1. What is the probability that a coin is flipped and land heads up and then a face card is pulled from a deck of 52?
2. If a 4 is rolled with a single six-sided die, what is the probability of all three events occurring?
3. What is the probability of two aces
being drawn consecutively from a deck of 52 cards?
4. What is the probability of the third card drawn also being an ace?
5. What is the probability of drawing 3 cards at random which are all aces if each card is replaced between each drawing?
6. What is the probability of drawing 3 cards at random which are all aces if the cards are not replaced between drawing?
-
Show Step-by-step Solutions
Try the free
Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
- Math
- English Language Arts
- Graphic Organizers
- Social Studies
- Science
- Teacher Printables
- Holidays
- Foreign Language
What Are Independent and Dependent Events? Probability tells us the likelihood of an event taking place or not. It is represented between numbers 0 and 1, with 1 showing certainty and 0 representing impossibility of occurrence of an event. If the probability is a number closer to 1, it represents a higher likelihood of happening. However, if the number is closer to 0, then the event has fewer chances of taking place. In probability, the event is defined as the outcome of the experiment. These events can be classified as independent events and dependent events. Independent events are those events that occur freely of each other. In other words, the incidence of one event doesn't hinder or affect the occurrence of another event. For example, the outcomes of two rolling dies do not depend on each other. The outcome of one die doesn't affect or change the outcome of the second die. Two events are independent if one or more of the following are true. P(A|B) = P(A), P(B|A) = P(B), P(A ∩ B) = P(A) P(B) Dependent events are those events that rely on each other. In simpler words, the occurrence of one influence the incidence of the other event.
We look at the probability of events that have little to no connection to each other. We also look at events that basically caused by each other. These are very common situations to find your self in on a daily basis if you work is related to the finance field. The most common physical objects that are used with this math are marbles, cards, colored balls, and I often see pulling names out of a hat.
Get Free Worksheets In Your Inbox!
Click the buttons to print each worksheet and answer key.
Meet the Skill
Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed. Two events, A and B, are independent if the outcome or occurrence of the first event does not affect the probability or outcome of the second event.
Try the Skill
You choose two objects at random, without putting them back in. What is the probability that you get a sphere, a cube in any order?
Practice the Skill Twice
We have a bag that contains 7 letters A, B, C, D, E, F, G. You choose three objects at random, without putting them back in. What is the probability that you will get these outcomes?
Show the Skill
What is the probability of drawing an orange ball without putting it back. Then drawing a black ball?
Warm Up
This can make for great class discussions.
Independent Events: Introduction
Three cards are to be drawn from a standard deck of cards. Find the probability of drawing a Jack, then a 10 and a Ace, after replacing the other two.
Independent Events- Worksheet 1
In a file, there are 6 Math papers, 5 Geography papers, and 8 English papers. If you select three papers at random, what is the probability of getting English then a Geography paper from the file without replacing first paper?
Worksheet 2
In a middle school of 80 students, 42 girls and 38 boys. What is the probability that if two students were randomly chosen, the first is a boy and then a girl sequentially?
Cards At Random
If there are 21 people sitting in a bus, 7 are children, 11 are women and 3 are men. One person is selected and then replaced. Another person is selected from bus. What is the probability that first person is a woman and the other person is a man?
Independent Events Quiz
A bottle contains 15 marbles: 5 are grey, 7 are green and 3 are yellow. What is the probability for picking a grey and then a green marble without replacing first?
"Do Now"
What is the probability that a randomly selected 10 to 40 number is divisible by 2 and then divisible by 6 after replacing first?
Worksheet 1
Jay and Rex are playing tennis. Probability of Jay winning the tennis game is .45 So what is the probability of Rex winning?
Worksheet 2
Each of the letters in the word CONNECT are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be C?
Review
A jar contains 10 indigo cones, 12 red cones, and 4 grey cones and you pick one without looking. What is the probability that the cone will not be indigo?
Quiz
There are 11 marbles in a bag and 4 of them are green. If one marble is chosen, what is the probability that it will be green?
Warm Up
A number from 50 to 70 is drawn at random. What is the probability that the number drawn is not divisible by 5?