# Probability of Independent and Dependent Events Worksheets

When we encounter a problem that includes multiple events, in some form, in order to understand the possible outcomes and the probabilities of them we must understand the nature of the relationship between these events. If one event has no affect on the outcome of another event, we call that an independent event. If one of the events affects the outcome of another event, in anyway, we call this a dependent affect. This will change how we approach the math behind this. These worksheets and lessons show students how to decide which events are dependent and which are independent toward simple probability.

### Aligned Standard: HSS-CP.A.2

- Coffee and Shoes Step-by-step Lesson- Is buying shoes and coffee dependent on one another? I know I need coffee to do anything before 8 AM.
- Guided Lesson - Start with a simple probability and then its back to label events.
- Guided Lesson Explanation - The second and third question are just a slight bit of thinking.
- Practice Worksheet - I came up with some really out there situations for you to work with.
- Matching Worksheet - This is perfect for a five minute warm up with kids.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

These are all about labeling the situation which can be very helpful.

- Homework 1 - A sportswear shop has 3 knee-high, 4 low-cut, and 6 mid-cut packs of socks. Robin bought 2 packs of low-cut socks. Bob picks 2 packs of socks at random.
- Homework 2 - You roll a 6-sided die twice. What is the probability (as a percentage) of getting an even number and then a four?
- Homework 3 - Students in a classroom are voting for class president by secret ballot. Thomas submits a ballot, and then William does.

### Practice Worksheets

These now lead us to determining probabilities based on the situations.

- Practice 1 - Jenny has some flowers in a bucket. She picks a flower at random. Without putting the first flower back, she picks second flowers at random. Are these two events dependent or independent?
- Practice 2 - The local supermarket has 12 chocolate almond milks and 7 vanilla almond milks. Smith bought 1 chocolate almond milk and 3 vanilla almond milks. Missy gets to the store after Smith and randomly picks 2 almond milks.
- Practice 3 - There is a sale on red and green grapes. The store has 14 green and 20 red grape packages. Mike buys 3 packages of red grapes. The clerk replaces all of the package of grapes that Mike bought with new packages of grapes. Samantha randomly chooses a pack of grapes.

### Math Skill Quizzes

These are great examples of what we have seen on past tests.

- Quiz 1 - Daisy has 4 green balls and 4 white balls. What is the probability of picking a green ball randomly?
- Quiz 2 - Liza has 7 green pencils and 7 orange pencils. What is the probability of picking a green pencil randomly from the box?
- Quiz 3 - There are 10 laptops. 2 of them are Samsungs and the rest are Sonys. Steve picks a laptop at random. What is the probability of getting a Samsung?

### What is the Difference between Independent and Dependent Events?

Events are possible outcomes in an experiment or a situation that we are paying attention to. Statistics most commonly has events that can be classified as dependent or independent. As a matter of fact, the existence of one event can provide evidence about the other and hence clues about it to be either dependent or independent. Generally, an event is dependent when it provides information about the other event and is accepted to be independent if it offers no clue/information about any event following it. Lets take a deeper dive into the nature of each:

**Dependent Events:** One event must have an influence over another in order to be dependent. To put it simply, a dependent event will only be dependent when another event has occurred first, and it relies on that. This also applies in real-life scenarios. In real life, you are going on a vacation is totally dependent on the amount of money you save for the trip. In addition to having the available free time to do so.

**Independent Events:** An event is said to be independent when it's not in any way dependent on another event, or its probability of occurrence is dependent on a preceding event. There is simply no need for correlation or exposure affecting the outcomes here. For example, the color of your car or handbag has absolutely no effect on where you work and how you work.

### The Formulas We Use with This Skill

You will find that in most cases you will be looking for the probability of independent events more often than not. The equation used describes as: P (overall) = P (A) x P (B). Where A and B are the probability of the two events we are exploring. As you start to tackle more advanced forms of statistics you will start to run into dependent events. The formula used is the same, you just need to take account of the second event which by our diagram is variable B. This usually happens in samples where you pull from a pool of choices in event A, but you do not replace the selection in made in that first event (A). This ultimately affects the size of your sample for event (B). Just focus your attention to the prospective sample size in sample B and you should be good to go.