Tree DiagramsCalculate the probability of independent and dependent combined events using tree diagrams. 
1. In a box there are two red balls and seven yellow balls. On Monday Gavin picked a ball at random from the box, played with it then put it back. On Tuesday he picked a ball at random from the box.
a) Complete the tree diagram.
b) What is the probability that on both days he picked a red ball? ^{}/_{}
c) What is the probability that on both days he picked a yellow ball? ^{}/_{}
d) Calculate the probability that on Monday he picked a red ball and on Tuesday he picked a yellow ball.^{}/_{}
Red
Yellow
Red
Yellow
Red
Yellow
2. In a round tin there are three cream cakes and four plain cakes. In a square based tin there are seven 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 four lemon sweets and seven lime sweets. This morning Gavin ate one sweet from the packet before breakfast and he 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 \( \frac{1}{11}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{10}\) otherwise it is \( \frac{1}{9}\) (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 seven red, eight blue and nine 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
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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/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
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