Probability guideFormal Sciences

Probability study guide on one topic: clear rules, solved problems with dice, cards and draws, and exercises

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Probability study guide on one topic: clear rules, solved problems with dice, cards and draws, and exercises

Example result

Example for the Standard package

Study guide: solving linear equations, for students aged 13–14

The one rule

An equation is a balance. Whatever you do to one side, you do to the other, and the balance stays level. The goal is to get x alone on one side.

Worked example 3: the unknown on both sides

Solve 5x − 4 = 2x + 11.

  1. Move the x terms to one side: take 2x from both sides. 5x − 2x − 4 = 11, so 3x − 4 = 11.
  2. Move the numbers to the other side: add 4 to both sides. 3x = 15.
  3. Divide both sides by 3. x = 5.
  4. Check: 5 × 5 − 4 = 21 and 2 × 5 + 11 = 21. Both sides match.

Common mistake

In 3(x + 2) = 18, many students write 3x + 2 = 18. The 3 multiplies everything in the brackets: 3x + 6 = 18, so x = 4.

Exercises 7–10

  1. 4x + 3 = x + 18
  2. 2(x − 5) = 14
  3. 7 − x = 3x − 9
  4. 3(2x + 1) = 4x + 15

Answers: 7. x = 5 · 8. x = 12 · 9. x = 4 · 10. x = 6

Files: PDF and Word. The guide is for learning: we do not do homework or tests to be handed in.

Client: a parent whose daughter gets lost when an equation has brackets or the unknown on both sides. Task: a guide at middle school level that starts from the basics and builds up to those two cases. Standard package: up to 8 pages, 6 worked examples, 20 exercises with answers and a summary sheet. Excerpt below.

The client and all details are made up.

About this service

Probability problems are short to read and easy to get wrong, mostly because the learner counts the wrong outcomes or multiplies when they should add. This guide takes one topic, such as simple events, combined and conditional probability, tree diagrams and tables, permutations and combinations, Bayes' rule, expected value or the binomial distribution, and explains in plain words what is being counted and which rule applies. Problems with coins, dice, cards, draws and everyday situations are solved step by step, then come the usual traps and exercises with answers. Tree diagrams are set out as labelled branches in text and tables. Tell us the course and what is hard. The guide is for learning: we do not solve homework, tests or exams to be handed in, and the exercises are new ones. Check the notation against your course.

What is included

  • What you getA PDF and Word file on your probability topic: what is being counted and which rule applies, problems solved step by step, tree diagrams as labelled branches, common traps and exercises with answers. From Standard, a one-page summary sheet with the rules and formulas; in Premium, a 20-question self-check test and a separate answer key with short explanations.
  • What are we counting?Outcomes, events and all possible cases made clear
  • Add or multiplyWhen events are 'or', 'and', independent or not
  • Trees and tablesBranches and tables written out to follow every case
  • Common mistakesCounting twice, ignoring order, mixing up P(A|B) and P(B|A)
  • At your levelFrom first chances at school to a college course

How it works

  1. 1
    TopicYou name the topic, the level and what is hard
  2. 2
    WritingWe write the explanation, solved problems and exercises
  3. 3
    DeliveryYou get the guide in PDF and Word on the order page
  4. 4
    StudyYou practise with it and ask for changes within your package

What we need from you

The exact probability topic, the grade or course, the curriculum and textbook if there is one, the notation used, what the learner already knows and where they get confused, the language, and how the guide will be used. You may attach a syllabus, a list of topics or a page of class notes as Word or PDF files, up to 3. Please do not send graded homework, tests or exam papers to be solved.

We will ask you:

  • Which probability topic?
  • For what level?
  • What does the learner already know, and what is hard?
  • Which curriculum or textbook should it follow?
  • Language and how the guide will be used

Compare packages

BasicUp to 4 pages$8StandardUp to 8 pages$17PremiumUp to 15 pages with a test$33
Deadline1 day2 days3 days
Revisions123
Pagesup to 4up to 8up to 15
Worked examples3610
Exercises with answers102035
Summary sheetNoYesYes
Test and answer keyNoNoYes, 20 questions
SubjectProbabilityProbabilityProbability
OrderOrderOrder

Payment protection

You pay when you order, but the money is released only for accepted work.

  • Fixed priceThe package price does not change after you pay.
  • The money is reservedWhen you pay, the amount is only reserved. It is released to the service once you accept the work.
  • Checked before deliveryEvery result goes through a quality check before it reaches you, and you see it on the order page before accepting it.
  • Free revisionsAsk for changes within your brief as many times as the package allows.
  • Acceptance after 3 daysIf within 3 days of delivery you neither accept the work nor ask for changes, it is accepted automatically. If you write in the order chat after delivery, the order waits; once we answer, we may start the 3 days again and will say so in the chat.
  • Redo or a full refundIf the result does not match your brief and the revisions did not fix it, or the work takes more than twice its deadline, write in the order chat: we will redo the work or refund the payment in full.
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Questions and answers

Can you solve my probability homework?

No. The guide teaches the rules with new problems and exercises; we do not solve homework, tests or exams to be handed in as your own work.

Are tree diagrams drawn?

They are set out as labelled branches with probabilities in text and tables, which is easy to copy onto paper. We don't promise drawn pictures.

Can it cover combinations and permutations?

Yes, as a topic of their own; they are often the hardest part. One order covers one topic.

Will it match my course?

We follow the level, curriculum and textbook you name, but programmes, notation and methods differ, so the learner or a teacher should check the guide against the course.

Can a teacher use it with a class?

Yes. Print it and share it with your learners; in Premium the test and the answer key are separate files, so you can hand out the test alone.

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