Worksheet: Tree Diagrams

In this worksheet, we will practice representing a sample space using a tree diagram.

Q1:

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

  • A 𝑆 = { T , T }
  • B 𝑆 = { H , H }
  • C 𝑆 = { H T , T H }
  • D 𝑆 = { H , T }
  • E 𝑆 = { T T , H H }

Q2:

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

  • A 𝐴 = { ( , , ) } H H H
  • B 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) } T H H T H T T T H T T T
  • C 𝐴 = { ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H
  • D 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H H T T

Q3:

Upon flipping a coin three consecutive times, use a tree diagram to determine the event 𝐴 that includes all of the outcomes where, at most, two tails are flipped.

  • A 𝐴 = { ( , , ) , ( , , ) , ( , , ) } H T T T H T T T H
  • B 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H T H H
  • C 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) } H T T T H T T T H T T T
  • D 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H H T T T H H T H T T T H

Q4:

If two spinners are spun, where the first is numbered from 1 to 2 and the second from 1 to 9, determine the probability of both spinners stopping at even numbers using a tree diagram.

  • A8 out of 18
  • B9 out of 11
  • C14 out of 18
  • D4 out of 18
  • E5 out of 11

Q5:

Mariam 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.

Q6:

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.

Base Cheese Sauce Topping (at most one)
Thin crust or deep pan Cheddar or mozzarella Tomato or barbecue Pepperoni, pineapple, or mushroom

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

Q7:

Suppose two spinners are spun. The first spinner is numbered from 1 to 3 and the second from 1 to 9. Using a tree diagram, determine what the probability of the sum of both spins being greater than 4 is.

  • A24 out of 27
  • B3 out of 36
  • C6 out of 27
  • D21 out of 27

Q8:

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?

  • A 𝐴 = { ( , , ) } H H H
  • B 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H T H T H H T T T H H T H T T T H T T T
  • C 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H H T T T H H T H T T T H
  • D 𝐴 = { ( , , ) } T T T

Q9:

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

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

Q10:

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 { 3 3 , 7 7 }
  • B { 3 7 , 7 3 }
  • C { 3 7 3 , 7 3 7 , 3 3 7 , 7 7 3 }
  • D { 3 7 , 3 3 , 7 3 , 7 7 }
  • E { 3 7 3 , 7 3 7 }

Q11:

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

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

Q12:

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

  • A 𝐴 = { ( , , ) , ( , , ) , ( , , ) } H T T T H T T T H
  • B 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H T H H
  • C 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) , ( , , ) } H H H H H T H T H H T T T H H T H T T T H
  • D 𝐴 = { ( , , ) , ( , , ) , ( , , ) , ( , , ) } H T T T H T T T H T T T

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