Lesson Worksheet: Tree Diagrams Mathematics • 7th Grade

In this worksheet, we will practice drawing and using tree diagrams.


Write the sample space 𝑆 for whether a regular coin lands heads side up (H) or tails side up (T) when flipped.

  • A𝑆={,}HT
  • B𝑆={,}HTTH
  • C𝑆={,}HH
  • D𝑆={,}TTHH
  • E𝑆={,}TT


A coin is flipped three consecutive times. Which of the following represents the event of getting a head on the first flip?

  • A𝐴={(,,),(,,),(,,),(,,)}HHHHHTHTHHTT
  • B𝐴={(,,),(,,),(,,)}HHHHHTHTH
  • C𝐴={(,,),(,,),(,,),(,,)}THHTHTTTHTTT
  • D𝐴={(,,)}HHH


A coin is flipped 3 times. Use the following tree diagram to determine the event 𝐴 that includes all of the outcomes where no more than two tails are flipped.

  • A𝐴={(,,),(,,),(,,),(,,),(,,),(,,),(,,)}HHHHHTHTHHTTTHHTHTTTH
  • B𝐴={(,,),(,,),(,,)}HTTTHTTTH
  • C𝐴={(,,),(,,),(,,),(,,)}HTTTHTTTHTTT
  • D𝐴={(,,),(,,),(,,),(,,)}HHHHHTHTHTHH


Hannah has drawn a tree diagram to represent the sample space of tossing two coins.

By extending the tree diagram or otherwise, find the number of outcomes in the sample space of the experiment of tossing two coins and spinning two spinners: one with 10 equal sections labeled 1 to 10 and one with 12 equal sections labeled 1 to 12.


A pizza parlor offers customizable pizzas. Customers can choose one of two options for the base, cheese, and sauce and then add an optional topping.

BaseCheeseSauceTopping (at Most One)
Thin crust or deep panCheddar or mozzarellaTomato or barbecuePepperoni, pineapple, or mushroom

Using tree diagrams, or otherwise, represent all the possible pizza combinations and determine how many different pizzas there are.


A fair coin is flipped three times and the results are recorded, writing H for heads and T for tails. Which of the following represents the event of getting no heads?

  • A𝐴={(,,),(,,),(,,),(,,),(,,),(,,),(,,)}HHTHTHHTTTHHTHTTTHTTT
  • B𝐴={(,,)}TTT
  • C𝐴={(,,)}HHH
  • D𝐴={(,,),(,,),(,,),(,,),(,,),(,,),(,,)}HHHHHTHTHHTTTHHTHTTTH


Which of the following describes the sample space of a random experiment?

  • AAn experiment which we can determine all its possible outcomes.
  • BThe set of all impossible outcomes of a random experiment.
  • CThe set of some possible outcomes of a random experiment.
  • DThe set of all possible outcomes of a random experiment.


I write a two-digit number by randomly picking each digit to be either 3 or 7, where digits can be repeated. Write the set of all possible outcomes.

  • A{37,33,73,77}
  • B{373,737}
  • C{37,73}
  • D{33,77}
  • E{373,737,337,773}


A bag contains 7 balls which are numbered 1 to 7. Determine the sample space of choosing a ball at random.

  • A{1,2,6,4,5,7}
  • B{1,2,3,4,5,6,7}
  • C{3,1,2,5,4,7}
  • D{1,5,6,2,3,7,8}


A coin is flipped three times. Which of the following is the event that at least two tails appear?

  • A𝐴={(,,),(,,),(,,)}HTTTHTTTH
  • B𝐴={(,,),(,,),(,,),(,,)}HTTTHTTTHTTT
  • C𝐴={(,,),(,,),(,,),(,,)}HHHHHTHTHTHH
  • D𝐴={(,,),(,,),(,,),(,,),(,,),(,,),(,,)}HHHHHTHTHHTTTHHTHTTTH

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