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Worksheet: Tree Diagrams

Q1:

Madison 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.

Q2:

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.

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

The given probability tree shows two events: 𝐴 and 𝐡 . 𝐴 is the event of it raining and 𝐡 is the event of a group of friends playing football.

Determine the probability of the friends playing football given that it rains.

Determine the probability of the friends playing football and it raining.

Determine the probability of the group of friends playing football irrespective of whether it rains.

Q9:

A fair coin is flipped twice and the results are recorded, writing H for heads and T for tails. Which of the following represents the sample space of this random experiment?

  • A { , } H T T H
  • B { , } H H T T
  • C { , , , } H H H T H T T T
  • D { , , , } H H H T T H T T

Q10:

Which experiment can be modelled by this tree diagram?

  • Atossing three coins
  • Btossing eight coins
  • Ctossing a coin eight times
  • Dtossing a coin three times

Q11:

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

Q12:

A fair coin is flipped and a fair die is rolled. Which of the following represents the event of getting a head on the coin and rolling and odd number on the die?

  • A 𝐴 = { ( , 1 ) , ( , 3 ) , ( , 5 ) } T T T
  • B 𝐴 = { ( , 2 ) , ( , 4 ) , ( , 6 ) } H H H
  • C 𝐴 = { ( , 1 ) , ( , 1 ) , ( , 3 ) , ( , 3 ) , ( , 5 ) , ( , 5 ) } T H T H T H
  • D 𝐴 = { ( , 1 ) , ( , 3 ) , ( , 5 ) } H H H