# 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.

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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.]"

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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.

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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.

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