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Calculating Simple Probability

PROCEDURAL
Mathematics›Probability|Ages 10—11|ID: mt_Zt30Gxi-qp

Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations

Mastery Evidence

  • Calculate the probability of drawing a blue marble from a bag of 3 blue and 7 red as 3/10
  • Use the formula P(event) = favourable outcomes ÷ total outcomes to solve at least three different problems
  • Explain why increasing the number of favourable outcomes increases the probability

Assessment Prompt

“If there are 3 red and 7 blue balls in a bag, can [child] work out the probability of picking a red one and express it as a fraction in its simplest form?”

Prerequisites2

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  • The 0-to-1 Probability Scale hard

    Calculating probability using favourable/total outcomes requires understanding probability as a number on a 0-1 scale

    • Probability as a Fraction hard

      The formal 0-1 probability scale formalises the fractional representation of equally-likely outcomes introduced at age 9-10

      • Simple Chance Experiments soft

        Practical experiment experience provides the intuitive grounding that makes fractional probability representation meaningful

        • Pictograms and tally charts soft

          Recording probability experiment results in tally charts uses the data-recording skills taught in Data & Statistics

          • Pictograms and tally charts (age 6+) hard

            Constructing pictograms, tally charts, and bar charts requires these display vocabulary terms

          • Sorting into categories hard

            Constructing pictograms and tally charts requires classifying and counting objects first

            • Comparing groups: more or fewer soft

              Sorting categories by count benefits from ability to compare quantities

              • Counting objects to 20 soft

                Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

                • How Many in Total? hard

                  Answering 'how many?' requires the cardinality principle

                  • One-to-one counting hard

                    Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

                • One-to-one counting hard

                  Counting objects to answer 'how many?' requires one-to-one correspondence

            • Counting objects to 20 hard

              Counting objects in each category requires being able to count sets of objects

              • How Many in Total? hard

                Answering 'how many?' requires the cardinality principle

                • One-to-one counting hard

                  Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

              • One-to-one counting hard

                Counting objects to answer 'how many?' requires one-to-one correspondence

          • Sorting Data into Categories soft

            Data representation formats (pictograms, tally charts) support organising data

            • How Many in Total? soft

              Counting data in categories requires understanding cardinality

              • One-to-one counting hard

                Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

            • Pictograms and tally charts (age 6+) hard

              Organising and representing data requires data, tally, frequency, and category vocabulary

            • Sorting into categories hard

              Organising data in categories builds on classifying and counting objects in categories

              • Comparing groups: more or fewer soft

                Sorting categories by count benefits from ability to compare quantities

                • Counting objects to 20 soft

                  Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

                  • How Many in Total? hard

                    Answering 'how many?' requires the cardinality principle

                    • One-to-one counting hard

                      Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

                  • One-to-one counting hard

                    Counting objects to answer 'how many?' requires one-to-one correspondence

              • Counting objects to 20 hard

                Counting objects in each category requires being able to count sets of objects

                • How Many in Total? hard

                  Answering 'how many?' requires the cardinality principle

                  • One-to-one counting hard

                    Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

                • One-to-one counting hard

                  Counting objects to answer 'how many?' requires one-to-one correspondence

        • Likelihood Language hard

          Conducting probability experiments and describing results requires knowing the language used to describe likelihood

      • Unit fractions hard

        Expressing probabilities as unit fractions (1/6, 1/2, 1/3) requires prior knowledge of unit fractions from the Fractions domain

        • Fractions of amounts hard

          Finding fractions of discrete sets extends finding fractions of shapes/quantities

          • Finding halves and quarters (age 5+) hard

            Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters

            • What Is a Half? hard

              Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

              • Division as equal sharing hard

                Finding a half requires equal sharing into 2 groups — a division concept

                • Subtraction as taking away or separating hard

                  Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                  • How Many in Total? hard

                    Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                    • One-to-one counting hard

                      Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • What Is a Half? hard

            Working with fractions extends from Y1 understanding of halves

            • Division as equal sharing hard

              Finding a half requires equal sharing into 2 groups — a division concept

              • Subtraction as taking away or separating hard

                Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                • How Many in Total? hard

                  Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                  • One-to-one counting hard

                    Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • Division as equal sharing soft

            Finding fractions of quantities uses equal sharing (division)

            • Subtraction as taking away or separating hard

              Division as equal sharing/grouping requires understanding subtraction as taking away/separating

              • How Many in Total? hard

                Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                • One-to-one counting hard

                  Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • Fraction Notation hard

            Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator

        • Division as equal sharing soft

          Finding 1/4 of 12 objects connects to division as sharing equally

          • Subtraction as taking away or separating hard

            Division as equal sharing/grouping requires understanding subtraction as taking away/separating

            • How Many in Total? hard

              Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

              • One-to-one counting hard

                Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

      • Equally Likely Outcomes hard

        Using fractions to represent probability only makes sense for equally-likely outcomes, so the equally-likely concept must come first

        • Ordering Likelihoods hard

          Understanding what 'equally likely' means is a specific case of comparing likelihoods that requires the general comparison skill first

          • Likelihood Language hard

            Comparing and ordering likelihoods requires first knowing the vocabulary of likelihood (certain, likely, unlikely, impossible)

    • Comparing fractions soft

      Expressing probability as fractions, decimals, and percentages requires comparing and ordering fractions — a skill built in the Fractions domain

      • Decomposing a shape into more equal shares soft

        More shares = smaller helps understand why 1/5 < 1/3

        • Halves & Quarters of Shapes hard

          Comparing share sizes requires experience partitioning into halves and quarters

          • Finding halves and quarters (age 5+) hard

            Partitioning into fourths/quarters extends from Y1 understanding of quarters

            • What Is a Half? hard

              Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

              • Division as equal sharing hard

                Finding a half requires equal sharing into 2 groups — a division concept

                • Subtraction as taking away or separating hard

                  Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                  • How Many in Total? hard

                    Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                    • One-to-one counting hard

                      Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • What Is a Half? hard

            Partitioning shapes into halves extends from Y1 understanding of halves

            • Division as equal sharing hard

              Finding a half requires equal sharing into 2 groups — a division concept

              • Subtraction as taking away or separating hard

                Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                • How Many in Total? hard

                  Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                  • One-to-one counting hard

                    Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

      • Fractions on a number line hard

        Comparing fractions requires understanding them as numbers on a line

        • Fractions of amounts hard

          Placing fractions on number line requires knowing what fractions are

          • Finding halves and quarters (age 5+) hard

            Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters

            • What Is a Half? hard

              Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

              • Division as equal sharing hard

                Finding a half requires equal sharing into 2 groups — a division concept

                • Subtraction as taking away or separating hard

                  Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                  • How Many in Total? hard

                    Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                    • One-to-one counting hard

                      Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • What Is a Half? hard

            Working with fractions extends from Y1 understanding of halves

            • Division as equal sharing hard

              Finding a half requires equal sharing into 2 groups — a division concept

              • Subtraction as taking away or separating hard

                Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                • How Many in Total? hard

                  Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                  • One-to-one counting hard

                    Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • Division as equal sharing soft

            Finding fractions of quantities uses equal sharing (division)

            • Subtraction as taking away or separating hard

              Division as equal sharing/grouping requires understanding subtraction as taking away/separating

              • How Many in Total? hard

                Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                • One-to-one counting hard

                  Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • Fraction Notation hard

            Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator

        • Tenths soft

          Counting in tenths supports placing fractions on a number line

          • Fractions of amounts hard

            Tenths extend fraction understanding from halves, thirds, quarters

            • Finding halves and quarters (age 5+) hard

              Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters

              • What Is a Half? hard

                Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

                • Division as equal sharing hard

                  Finding a half requires equal sharing into 2 groups — a division concept

                  • Subtraction as taking away or separating hard

                    Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                    • How Many in Total? hard

                      Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                      • One-to-one counting hard

                        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

            • What Is a Half? hard

              Working with fractions extends from Y1 understanding of halves

              • Division as equal sharing hard

                Finding a half requires equal sharing into 2 groups — a division concept

                • Subtraction as taking away or separating hard

                  Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                  • How Many in Total? hard

                    Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                    • One-to-one counting hard

                      Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

            • Division as equal sharing soft

              Finding fractions of quantities uses equal sharing (division)

              • Subtraction as taking away or separating hard

                Division as equal sharing/grouping requires understanding subtraction as taking away/separating

                • How Many in Total? hard

                  Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

                  • One-to-one counting hard

                    Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

            • Fraction Notation hard

              Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator

          • Counting in 2s soft

            Skip counting supports counting in tenths

  • Equally Likely Outcomes hard

    The probability formula only applies to situations with equally likely outcomes — this concept must be secure first

    • Ordering Likelihoods hard

      Understanding what 'equally likely' means is a specific case of comparing likelihoods that requires the general comparison skill first

      • Likelihood Language hard

        Comparing and ordering likelihoods requires first knowing the vocabulary of likelihood (certain, likely, unlikely, impossible)

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