Tree DiagramsCalculate the probability of independent and dependent combined events using tree diagrams. |
1. In a box there are four red balls and seven yellow balls. On Monday Victoria picked a ball at random from the box, played with it then put it back. On Tuesday she picked a ball at random from the box.
a) Complete the tree diagram.
b) What is the probability that on both days she picked a red ball? /
c) What is the probability that on both days she picked a yellow ball? /
d) Calculate the probability that on Monday she picked a red ball and on Tuesday she picked a yellow ball./
Red
Yellow
Red
Yellow
Red
Yellow
2. In a round tin there are five cream cakes and four plain cakes. In a square based tin there are four cream cakes and five plain cakes. The tree diagram shows the probabilities of picking one cake from each tin.
a) Complete the tree diagram.
b) What is the probability of picking two cream cakes? /
c) What is the probability of picking two plain cakes? /
d) Calculate the probability of picking two different types of cake./
Cream
Plain
Cream
Plain
Cream
Plain
3. In a packet there are six lemon sweets and seven lime sweets. This morning Victoria ate one sweet from the packet before breakfast and she ate another after breakfast. Both sweets were picked randomly from what was in the packet at the time.
a) Complete the tree diagram.
b) What is the probability of picking two lemon sweets? /
c) What is the probability of picking a lemon sweet followed by a lime sweet? /
d) Calculate the probability of picking a lime sweet followed by a lemon sweet?./
Lemon
Lime
Lemon
Lime
Lemon
Lime
4. The probability that the first bus is late is \( \frac{1}{13}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{12}\) otherwise it is \( \frac{1}{11}\) (buses are either on time or late, they are never early!).
a) Complete the tree diagram.
b) What is the probability of both buses being late? /
c) What is the probability of both buses being on time? /
d) What is the probability of at least one bus being on time? /
Late
On Time
Late
On Time
Late
On Time
5. In a bag there are three red, four blue and five green counters. Two counters are taken out and not replaced.
a) Complete the tree diagram.
b) What is the probability of both counters being red? /
c) What is the probability of both counters not being red? /
d) What is the probability of at least one counter being red? /
Red
Not red
Red
Not red
Red
Not red
InstructionsTry 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. |
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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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