Tree Diagrams

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1. In a box there are two red balls and three yellow balls. On Monday Juan 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? / Correct Wrong
c) What is the probability that on both days he picked a yellow ball? / Correct Wrong
d) Calculate the probability that on Monday he picked a red ball and on Tuesday he picked a yellow ball./ Correct Wrong

Red

Yellow

Red

Yellow

Red

Yellow

\( \frac{2}{5} \)

\( \frac{3}{5} \)

\( \frac{}{} \)

\( \frac{2}{5} \)

\( \frac{}{} \)

Monday

Tuesday

2. In a round tin there are three cream cakes and six plain cakes. In a square based tin there are five cream cakes and seven 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? / Correct Wrong
c) What is the probability of picking two plain cakes? / Correct Wrong
d) Calculate the probability of picking two different types of cake./ Correct Wrong

Cream

Plain

Cream

Plain

Cream

Plain

\( \frac{3}{9} \)

\( \frac{}{} \)

Round Tin

Square Tin

3. In a packet there are four lemon sweets and five lime sweets. This morning Juan 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? / Correct Wrong
c) What is the probability of picking a lemon sweet followed by a lime sweet? / Correct Wrong
d) Calculate the probability of picking a lime sweet followed by a lemon sweet?./ Correct Wrong

Lemon

Lime

Lemon

Lime

Lemon

Lime

\( \frac{}{} \)

\( \frac{5}{9} \)

\( \frac{}{} \)

\( \frac{4}{8} \)

Before Breakfast

After Breakfast

4. The probability that the first bus is late is \( \frac{1}{14}\). If the first bus is late, the probability of the second bus being late is \( \frac{1}{13}\) otherwise it is \( \frac{1}{12}\) (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? / Correct Wrong
c) What is the probability of both buses being on time? / Correct Wrong
d) What is the probability of at least one bus being on time? / Correct Wrong

Late

On Time

Late

On Time

Late

On Time

\( \frac{}{} \)

First Bus

Second Bus

5. In a bag there are five red, six blue and seven 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? / Correct Wrong
c) What is the probability of both counters not being red? / Correct Wrong
d) What is the probability of at least one counter being red? / Correct Wrong

Red

Not red

Red

Not red

Red

Not red

\( \frac{}{} \)

First Counter

Second Counter

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

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