Conditional Probability

Menu Level 1 Exam Help More Probability

This is level 1: a mixed selection of conditional probability questions. You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

In a bookstore, there are two sections: fiction and non-fiction. In the fiction section, 50% of the books have hard covers, while in the non-fiction section, only 60% of the books have hard covers. If a customer picks a book at random and it has a hard cover, what is the probability that it is from the non-fiction section? Assume that there are an equal number of books in the fiction and non-fiction sections.

Give your answer to three significant figures.

☐ ☐ ✓ ✗

31 Scouts went hiking. 16 got lost, 18 got blisters, and 10 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.

Give your answer as a fraction.

☐ ☐ ✓ ✗

Every family in Happyland has either has a car or a motor scooter or both. 71% of the families have a car. 86% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.

Give your answer as a fraction.

☐ ☐ ✓ ✗

Box A contains 7 red and 10 blue cubes, and box B contains 11 red and 13 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B?

Give your answer as a fraction.

☐ ☐ ✓ ✗

What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 7% chance and machine B has a 9% chance of breaking down on any given day?

Give your answer to three significant figures.

☐ ☐ ✓ ✗

Each afternoon the probability my cat sleeps is 0.6 and the probability that my dog sleeps is 0.5. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon.

Give your answer to three significant figures.

☐ ☐ ✓ ✗

Tin A contains 7 red balls and 10 green balls. Tin B contains 11 red balls and 13 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.

Give your answer as a fraction.

☐ ☐ ✓ ✗

The probability that I drop and brake my phone when I visit a coffee shop is 0.11. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?

Give your answer to three significant figures.

☐ ☐ ✓ ✗

The probability that it is cloudy on a particular day is 0.6. The probability that it is cloudy with a high level of pollution on a particular day is 0.4. Find the probability that there will be a high level of pollution on a day when it is cloudy.

Give your answer to three significant figures.

☐ ☐ ✓ ✗

Given equal populations of Type X and Type Y bacteria, with mutation rates of 70% and 20% respectively, if a mutated bacterium is found, what's the probability it's Type Y?

Give your answer to three significant figures.

☐ ☐ ✓ ✗

Check

This is Conditional Probability level 1. You can also try:

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

	You are learning this because future ideas are built on previous ideas and the more ideas you learn the more power you have to learn anything, ever! The world's best football player engages in rigorous training, practicing skills repeatedly to prepare for the big game. While the specific actions rehearsed during these exercises are rarely needed in the match, the very process of performing these drills enhances their overall prowess as a top player. more...	More Activities: Maths Map Go Maths Games Puzzles Times Tables TablesMaster iPad Maths Investigations Exam Questions
Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales: "Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!" Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."		Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity Code Cracker Learn the basic techniques for cracking codes then practise them using this interactive challenge. There are three levels of difficulty and many different messages to decipher.	Answers There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe
Go Maths Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths Map Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.
Teachers
If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:	Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.	It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B!
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program

Conditional Probability:

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred. It represents the probability of event A happening, given that event B has already occurred. It is denoted as P(A|B), read as "the probability of A given B."

The formula for conditional probability is:

$$P(A|B) = \frac{{P(A \cap B)}}{{P(B)}}$$

Where:

$P(A|B)$ is the conditional probability of event A given event B,

$P(A \cap B)$ is the probability of both events A and B occurring,

$P(B)$ is the probability of event B occurring.

Help Video

This video is from Revision Village

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

❎

Conditional Probability

Find the probability of one event happening given that another event has already happened.

Menu Level 1 Exam Help More Probability

Instructions

More Activities:

Featured Activity

Code Cracker

Answers

Go Maths

Maths Map

Teachers

Description of Levels

Conditional Probability:

Help Video