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Probability practice

Two dice probability worksheets

Count ordered outcomes from two fair dice. Practice number events, sums, differences, products and factor relationships with probabilities derived from all 36 possible pairs.

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Treat the first and second dice as distinguishable. Count matching ordered pairs out of the 36 equally likely outcomes, then simplify.

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A4

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Count the outcomes that match the event

Each question makes its experiment and event explicit. The answer key connects the favorable count with the whole sample space, then simplifies the fraction. Selected question families control what appears on the sheet.

A probability is a property of the stated model. When outcomes are not equally likely, a simple count of different labels is not enough. With two dice, use 36 ordered pairs rather than eleven possible sums.

Learning objective

What this activity builds

Use ordered pairs to calculate compound-event probabilities without assuming that sums are equally likely.

Worked example

Two fair six-sided dice are rolled independently. What is the probability that their sum is 7?

6/36 = 1/6.

The six matching pairs are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1). There are 6 × 6 = 36 equally likely ordered outcomes. A sum of 2 has only one matching pair, so the possible sums do not all have the same chance.

Teaching notes

Make the practice count

  • Use two different colored dice to make order visible.
  • Build a 6-by-6 outcome table and mark the matching cells.
  • For an absolute difference, compare the larger and smaller values.
  • Distinguish at least one matching die from both dice matching.

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The two dice are distinguishable, so the sample space has 36 ordered outcomes. Sums are counted from those outcomes.

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Math SheetNameScore/ 10TeacherDateTwo Dice ProbabilityUse the stated equally likely outcomes. Give each probability as a simplified fraction.1.AB1–6Roll two distinguishable fair six-sideddice.How many ordered outcomes are in the sample space?2.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of not (first die divides 17) and not(second die divides 17)?3.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of product = 37?4.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of not (sum = 7)?5.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of not (absolute difference = 1)?6.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of first die: even?7.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of product is a multiple of 1?8.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of second die: even?9.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of first die: even and second die:even?10.AB1–6Roll two distinguishable fair six-sideddice.What is the probability of first die divides 60 and seconddie divides 60?math-sheet.comPage 1 / 1

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