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Tree Diagrams

Calculate the probability of independent and dependent combined events using tree diagrams.
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This is level 2: more probability questions requiring you to draw your own tree diagrams. You will be awarded a trophy if you get at least 9 correct and you do this activity online. Fractions should be given in their lowest terms.

1

The probability that the daily flight from New York will be more than an hour late is 0.3.

(a) What is the probability that the fight will not be more than an hour late on both Monday and Tuesday?

= ☐ ✓ ✗

(b) What is the probability that the fight will be more than an hour late on at least one of the first two days of this week?

= ☐ ✓ ✗

2

Two tins contain plastic cubes.
One tin contains three blue cubes and seven orange cubes the other tin contains two orange cubes and three blue cubes.
Owen chooses a tin at random and from it randomly takes out a cube.
What is the probability that the cube Owen chooses is blue?

=

 ☐ ✓ ✗
3

A bag contains three red pens, five blue pens and a black pen. Zoe takes out one pen at random for her school work one morning but does not put it back in the bag. That afternoon she takes another pen out of the bag.

What is the probability that the two pens chosen that day were of the same colour?

=

 ☐ ✓ ✗
4

The Celebrate Greetings Card Company sell a wholesale pack of colourful cards. The cards are produced such that 40% are square, 35% are triangular and 25% are circular. It is known that 20% of the square, 10% of the triangular and 50% of the circular cards are classified as Humorous.

(a) If a card is selected at random from the pack what is the probability that it is triangular and Humerous?

= ☐ ✓ ✗

(b) If a card is selected at random from the pack what is the probability that it is round and not Humorous?

= ☐ ✓ ✗

(c) If a card is selected at random from the pack what is the probability that it is Humorous?

= ☐ ✓ ✗

(d) If a card is selected at random from the pack what is the probability that it is not a humorous square card?

= ☐ ✓ ✗

5

Three playing cards, a King, a Queen and a Jack are shuffled and one is chosen at random. This process is repeated two more times.

(a) What is the probability that the cards chosen are all Queens?

=

 ☐ ✓ ✗





(b) What is the probability that only one of the three cards chosen is a Jack?

=

 ☐ ✓ ✗





(c) What is the probability that at least one King is chosen?

=

 ☐ ✓ ✗
6

Vanessa travels to school each week day by bus or by car. The car option is only available if her cousin is available to drive which only happens on 30% of the days.

What is the probability that next week her mode of travel to school will not be the same on any two consecutive days?

= ☐ ✓ ✗

Check

This is Tree Diagrams level 2. You can also try:
Level 1 Level 3

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Kinglsley, Tanzania

Thursday, May 9, 2024

"One of the answers in Level 2 is wrong. The answer is supposed to be 12/27.

[Transum: Thank you for your feedback Kinglsley. If 12/27 is the correct probability it should be typed in as a faction in its lowest terms. I can see the numerator and the denominator are both multiples of three.]"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Description of Levels

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Level 1 - Basic probability questions for which the tree diagram has already been drawn

Level 2 - More probability questions requiring you to draw your own tree diagrams

Level 3 - A challenging puzzle that can be solved with the aid of a tree diagram

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Example

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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