⭐ COUPON: SALE2020 ⭐ 20% OFF ON ALL WORKBOOKS*3 DAYS FREE SHIPPING ⭐ FREE RETURNS ⭐

Fail to load the data
0

Probability and chance surround us every day. If you have ever watched the news, the weather and market trends are given as probabilities. The chance of rain or snow is a great example of probability in everyday life.

Before going over independent and mutually exclusive events, let’s review some important probability vocabulary.

Vocabulary

Probability: The likeliness that an event will occur. It is measured by the favorable outcomes over the total possible outcomes.

Event: An event is an outcome or a set of outcomes of an experiment.
Sample Space: The set of all possible outcomes of an experiment.

Types of Events

A mutually exclusive event is a situation in which two events cannot occur at the same time.

Independent events are when one event is unaffected by another event.
Dependent events are when one event affects the outcome of another event.

Simple: An event with a single outcome
Compound: Two independent events occurring. Found by multiplying the probabilities of the events.

Let’s take a look at flipping a coin. When you flip a coin there are two possible outcomes. One outcome is the coin lands on heads, the second outcome is that the coin lands on tails.

The experiment is flipping the coin. The sample space for this experiment is heads and tails.

When you flip a coin once you cannot get both heads and tails. This means that the events of getting heads or getting tails are mutually exclusive.

This is also a simple event since there is one event that is taking place.

Notice that with the diagram, there is no overlap between the two events.

Now let’s say you are going to roll a standard six sided die and flip a coin.

Since there are two events this is now a compound event. If you land on four with the die, that does not affect what the coin will land on. These two events are independent.

Keeping with the numbered die, two events that would not be mutually exclusive would be rolling an odd number and rolling a 5.

Rolling a 3 would satisfy one of the events, rolling an odd. However, if a 5 is rolled, it satisfies both events and happens at the same time.

Notice the overlap with these events. There are numbers that are odd that are not five, but a five is always odd.

 

Did you know?

  • Mutually exclusive events are always dependent.
  • The probability of two people in a room of 23 people having the same birthday is 50%
  • A probability of 0 means that the event is impossible
  • A probability of 1 means that the event is a certainty.

Probability Notation

What is the probability of rolling a 4 with a standard six sided die? Let’s start by looking at the sample space, the different numbers that the die can land on.

Sample Space: 1, 2, 3, 4, 5, 6

The favorable outcome for this experiment is 4.

Example 1:

What is the probability of flipping a tail and rolling an even number?

Let’s start with the probability of flipping a tail.

Next, what is the probability of rolling an even number?

To find the probability of these independent events, the probabilities are multiplied.

Example 2:

What is the probability of flipping both a tail and heads with one coin?

Since only one coin is being used, you can only get one result, this means that the events are mutually exclusive.

Example 3:

What is the probability of choosing an ace or a queen from a standard deck of cards?

You can also look at the number of favorable outcomes, 8, over the total number of cards, 52. This will also reduce to become .

Example 4:

Given a standard deck of cards.
Let H = choosing a heart
Let E = choosing an even number
Let F = choosing a five
Let A = choosing an Ace

Which of the following are mutually exclusive events?

Start with H and compare it to the other events.

  • Can a card be both a heart and an even? Yes
  • Can a card be both a heart and a five? Yes
  • Can a card be both a heart and an Ace? Yes

Next look at E.

  • Can a card be both an even and a five? No- mutually exclusive events
  • Can a card be both an even and an Ace? No – mutually exclusive events

The last pairing is F and A

  • Can a card be both a five and an ace? No – mutually exclusive events     

Practice:

Are the following mutually exclusive events?

  1. Pulling one card and getting a King and Ace from a standard deck of cards
  2. Rolling a dice and getting an even and the number 6
  3. Pulling an Ace and a diamond from a standard deck of cards.

Are the following independent events?
1. Flipping a coin and spinning a spinner

2. Choosing a marble from a bag, not replacing it, and then choosing another marble.


Three cards, the queen of hearts, 5 of diamonds, and queen of spades, were chosen
from a standard deck of cards. Can you tell if these events were dependent or
independent?


Three cards, the queen of spades, 5 of diamonds, and queen of spades, were chosen
from a standard deck of cards. Can you tell if these events were dependent or independent?


Given a standard deck of cards.

  • Let H = choosing a spade
  • Let E = choosing an odd number
  • Let F = choosing a eight
  • Let A = choosing a King

Which combination of two events are mutually exclusive events?


Which of the following is mutually exclusive?

a.

b.

Frequently Asked Questions

The capital P means probability. What is inside of the parenthesis is the event that is the favorable outcome for the experiment. This notation is asking, “what is the probability of getting tails.”

Mutually exclusive means that two events cannot happen at the same time. You can’t make both a right turn and a left turn at the same time. You can’t roll both an even and an odd number on a single die at the same time.

Independent events are two events in which the outcome of one event doesn’t affect the outcome of another event. If you flip two coins, whatever the first coin landed on will not affect how the second coin will land.

The probability of an event is found by creating a ratio of the number favorable outcomes over the total number of outcomes.

In order to tell if an event is dependent is to see if the outcome of the first event affects the outcome of the second event. Are items chosen and then not replaced? This is an indication of dependent events because the total number of outcomes changes from the first event to the second event. If a card is removed from a deck and not replaced the total number of cards went from 52 to 51. That changes the second outcomes probability.

The sample space is the set of all of the possible outcomes. This is often a list, not a number. The sample space for flipping a coin is heads or tails, . The total number of possible outcomes is 2. A list of outcomes can not be used to create a ratio for probability.

What do you think about this article? Share your opinion with us

ENTER BELOW FOR ARGOPREP'S FREE WEEKLY GIVEAWAYS. EVERY WEEK!
Great! You will receive an email from US shortly. Have a great day!
FREE 100$ in books to a family!
Error! Please try again!
SUCCESS
See Related Worksheets:
2nd grade
Fishing for Fractions with Feline Fiona
Worksheets
 (0)
Feline Fiona is fishing for fractions! Each shape is partitioned into equal parts. Students will use the provi...
2nd grade
Top Ten Addition
Worksheets
 (0)
This math worksheet is sure to be in your top ten! Learners use the brightly colored pictures and for groups o...
2nd grade
Cotton Candy Counts and Compares
Worksheets
 (0)
Math is both magical and delicious with this adorable "llamacorn" named Cotton Candy! Students will love filli...
1st grade
Is It Snack Time in the Sea, Yet?
Worksheets
 (0)
Sea creatures are pretty clever, but they do struggle to tell time with analog clocks. They need your help! Ca...
2nd grade
"School" Days and Sight Words
Worksheets
 (0)
"School" days become fun days when filled with sight words! An important reading skill, this colorful workshee...
1st grade
Trace Letter "N"
Worksheets
 (0)
Ready to take your teaching methodologies to new heights? Let our trace the letter “N” worksheet be your s...

Try ArgoPrep for FREE

Learn more Try ArgoPrep for FREE

Share good content with friends and get 15% discount for 12-month subscription

Share in facebook Share in twitter

Read More

Loading content ...
Loading failed...
Exclusive Offer To Boost Your Scores!
Want 800+ Printable Math Questions?
Absolutely For Free 🥳