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Worksheet: Using Tree Diagrams to Count Outcomes

Q1:

In probability, what is an outcome defined as?

  • Aa repeatable process, or activity, which can result in different events occurring
  • Bthe set of all possible things that can happen as a result of an activity or experiment
  • Ca possible result of an activity or experiment

Q2:

In an experiment, this spinner is spun. List all the possible outcomes.

  • A 2 , 6 , 5 , 8
  • B 2 , 6 , 5 , 8 , 3
  • C 2 , 6 , 5
  • D 2 , 6 , 5 , 8 , 3 , 4
  • E 2 , 6

Q3:

In an experiment, this spinner is spun. List all the possible outcomes.

  • A 2 , 9 , 7 , 5
  • B 2 , 9 , 7 , 5 , 3
  • C 2 , 9 , 7
  • D 2 , 9 , 7 , 5 , 3 , 8
  • E 2 , 9

Q4:

In an experiment, this spinner is spun. List all the possible outcomes.

  • A 1 , 8 , 7 , 4
  • B 1 , 8 , 7 , 4 , 0
  • C 1 , 8 , 7
  • D 1 , 8 , 7 , 4 , 0 , 5
  • E 1 , 8

Q5:

In an experiment, this spinner is spun. List all the possible outcomes.

  • A 4 , 9 , 2 , 1
  • B 4 , 9 , 2 , 1 , 3
  • C 4 , 9 , 2
  • D 4 , 9 , 2 , 1 , 3 , 0
  • E 4 , 9

Q6:

If the shown spinner was spun once and a coin was tossed once, determine the number of possible outcomes.

Q7:

If the shown spinner was spun once and a coin was tossed once, determine the number of possible outcomes.

Q8:

If the shown spinner was spun once and a coin was tossed once, determine the number of possible outcomes.

Q9:

List all the possible outcomes when spinning this spinner.

  • A 𝑃 , 𝑇 , 𝑉
  • B 𝑃 , 𝑇 , 𝑉 , π‘ˆ
  • C 𝑃 , 𝑇
  • D 𝑃 , 𝑇 , 𝑉 , π‘ˆ , 𝑄
  • E 𝑃

Q10:

List all the possible outcomes when spinning this spinner.

  • A 𝑅 , 𝑇 , 𝑉
  • B 𝑅 , 𝑇 , 𝑉 , 𝑄
  • C 𝑅 , 𝑇
  • D 𝑅 , 𝑇 , 𝑉 , 𝑄 , 𝑃
  • E 𝑅

Q11:

Daniel is going to spin both of these spinners and record the two letters that appear.

Which of the following tree diagrams shows the sample space of the letter pairs?

  • A
  • B
  • C
  • D

How many possible outcomes are there?

Find the probability of getting 𝐴 or 𝐡 on spinner 1 and 𝐷 on spinner 2. Give your answer as a fraction in its simplest form.

  • A 1 6
  • B 1 1 2
  • C 1 9
  • D 1 3

Q12:

A class have a die with the numbers 1, 2, 3, 4, 5, and 6 and a spinner with the numbers 2, 4, 6, and 8. They are going to roll the die and spin the spinner and find the sum of the two numbers that appear. They started to complete a two-way table to model the sample space.

Die
1 2 3 4 5 6
Spinner 2 3 4 5 6 7 8
4 5 6 7 8
6 7 8
8 9 10

How many possible outcomes are there?

By completing the table, find the probability of the sum being a number greater than 10.

Give your answer as a fraction in its simplest form.

  • A 1 4
  • B 1 6
  • C 1 5
  • D 1 3
  • E 2 5

Q13:

The image shows a fair spinner.

Daniel wanted 5 random numbers from 1 to 5, so he spun the spinner 5 times. His results were 1, 2, 3, 4, and 5.

Which of the following statements is true about his results?

  • AThey are not random numbers because the results came in order of size, which is unlikely.
  • BThey are random numbers because the spinner is fair and he got one of each number.
  • CThey are not random numbers because you would expect some numbers to come up more than others.
  • DThey are random numbers because the spinner is fair and was spun randomly.
  • EThey are random numbers because you would expect each number to appear once.

Q14:

A pair of numbers is obtained by spinning this spinner once and rolling a number cube. How many possible outcomes are there?