Tree diagrams (basic)

Authored by Stephen Langford

Mathematics

8th Grade

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10 questions

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DRAG AND DROP QUESTION

45 sec • 1 pt

On a tree diagram,
the (a) are written at the ends of the branches,
the (b) are written above / below the branches.

outcomes

probabilities

FILL IN THE BLANKS QUESTION

30 sec • 1 pt

For any set of branches on a tree diagram, the probabilities must add up to what number?

(a)

MATH RESPONSE QUESTION

30 sec • 1 pt

The diagram shows an incomplete set of branches of a tree diagram.
What is the missing number?

$0.7$

Mathematical Equivalence

MATH RESPONSE QUESTION

30 sec • 1 pt

The diagram shows an incomplete set of branches of a tree diagram.
What is the missing number?

$\frac{3}{5}$

Mathematical Equivalence

OFF

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What calculation works out the probability the coin lands on Heads twice?

$0.4\times0.4$

$0.4+0.4$

$0.4\times2$

$0.4\div0.4$

MATH RESPONSE QUESTION

45 sec • 1 pt

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What is the probability the coin lands on Heads twice?

$0.16$

Mathematical Equivalence

Answer explanation

We multiply the numbers on the branches, so here we do 0.4 x 0.4 = 0.16

MATH RESPONSE QUESTION

45 sec • 1 pt

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What is the probability the coin lands on Tails twice?

$0.36$

Mathematical Equivalence

Answer explanation

We multiply the numbers on the branches, so here we do 0.6 x 0.6 = 0.36

MATH RESPONSE QUESTION

1 min • 1 pt

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What is the probability the coin lands on Heads exactly once?

$0.48$

Mathematical Equivalence

Answer explanation

Landing on Heads once can happen in 2 ways, Heads then Tails, or Tails then Heads.
Head then Tails = 0.4 x 0.6 = 0.24
Tails then Heads = 0.6 x 0.4 = 0.24
Total probability = 0.24 + 0.24 = 0.48

MATH RESPONSE QUESTION

45 sec • 1 pt

A dice is biased so that the probability it lands on a six is $\frac{2}{7}$
The dice is rolled twice, the partly completed tree diagram shows some of the possible outcomes.
What is the probability the dice lands on a six twice?

$\frac{4}{49}$

Mathematical Equivalence

OFF

Answer explanation

On each set of branches, the probability of getting a six is 2/7
We multiply the numbers on the branches, so here we do 2/7 x 2/7 = 4/49

10.

MATH RESPONSE QUESTION

1 min • 1 pt

A dice is biased so that the probability it lands on a six is $\frac{2}{7}$
The dice is rolled twice, the partly completed tree diagram shows some of the possible outcomes.
What is the probability the dice lands on a six at least once?

$\frac{24}{49}$

Mathematical Equivalence

OFF

Answer explanation

Landing on a six at least once means we could get one six or two sixes.
We can get one six in 2 different ways:
Six, not six = 2/7 x 5/7 = 10/49
Not six, six = 5/7 x 2/7 = 10/49
We can get two sixes in only one way:
Six, six = 2/7 x 2/7 = 4/49
Total probability = 10/49 + 10/49 + 4/49 = 24/49
Note: we can calculate this more quickly by thinking about the opposite event - if we do NOT get at least one six that means we get no sixes. Not six, not six = 5/7 x 5/7 = 25/49
So our event has probability 1 - 25/49 = 24/49

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Tree diagrams (basic)

On a tree diagram, the​ (a) are written at the ends of the branches, the ​ (b) are written above / below the branches.

For any set of branches on a tree diagram, the probabilities must add up to what number? (a)

The diagram shows an incomplete set of branches of a tree diagram.What is the missing number?

The diagram shows an incomplete set of branches of a tree diagram.What is the missing number?

A coin is biased so that the probability it lands on Heads is 0.40.40.4 The coin is flipped twice, the tree diagram shows the possible outcomes. What calculation works out the probability the coin lands on Heads twice?

A coin is biased so that the probability it lands on Heads is 0.40.40.4 The coin is flipped twice, the tree diagram shows the possible outcomes. What is the probability the coin lands on Heads twice?

We multiply the numbers on the branches, so here we do 0.4 x 0.4 = 0.16

A coin is biased so that the probability it lands on Heads is 0.40.40.4 The coin is flipped twice, the tree diagram shows the possible outcomes. What is the probability the coin lands on Tails twice?

We multiply the numbers on the branches, so here we do 0.6 x 0.6 = 0.36

A coin is biased so that the probability it lands on Heads is 0.40.40.4 The coin is flipped twice, the tree diagram shows the possible outcomes. What is the probability the coin lands on Heads exactly once?

Landing on Heads once can happen in 2 ways, Heads then Tails, or Tails then Heads.Head then Tails = 0.4 x 0.6 = 0.24Tails then Heads = 0.6 x 0.4 = 0.24Total probability = 0.24 + 0.24 = 0.48

A dice is biased so that the probability it lands on a six is 27\frac{2}{7}72​ The dice is rolled twice, the partly completed tree diagram shows some of the possible outcomes. What is the probability the dice lands on a six twice?

On each set of branches, the probability of getting a six is 2/7We multiply the numbers on the branches, so here we do 2/7 x 2/7 = 4/49

A dice is biased so that the probability it lands on a six is 27\frac{2}{7}72​ The dice is rolled twice, the partly completed tree diagram shows some of the possible outcomes. What is the probability the dice lands on a six at least once?

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Discover more resources for Mathematics

On a tree diagram,
the (a) are written at the ends of the branches,
the (b) are written above / below the branches.

For any set of branches on a tree diagram, the probabilities must add up to what number?

(a)

The diagram shows an incomplete set of branches of a tree diagram.
What is the missing number?

The diagram shows an incomplete set of branches of a tree diagram.
What is the missing number?

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What calculation works out the probability the coin lands on Heads twice?

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What is the probability the coin lands on Heads twice?

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What is the probability the coin lands on Tails twice?

A coin is biased so that the probability it lands on Heads is $0.4$
The coin is flipped twice, the tree diagram shows the possible outcomes.
What is the probability the coin lands on Heads exactly once?

Landing on Heads once can happen in 2 ways, Heads then Tails, or Tails then Heads.
Head then Tails = 0.4 x 0.6 = 0.24
Tails then Heads = 0.6 x 0.4 = 0.24
Total probability = 0.24 + 0.24 = 0.48

A dice is biased so that the probability it lands on a six is $\frac{2}{7}$
The dice is rolled twice, the partly completed tree diagram shows some of the possible outcomes.
What is the probability the dice lands on a six twice?

On each set of branches, the probability of getting a six is 2/7
We multiply the numbers on the branches, so here we do 2/7 x 2/7 = 4/49

A dice is biased so that the probability it lands on a six is $\frac{2}{7}$
The dice is rolled twice, the partly completed tree diagram shows some of the possible outcomes.
What is the probability the dice lands on a six at least once?