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IB Math Studies Yr 1

Name_________________________________

Date: ____________

Using Tree Diagrams Example: What is the probability of a flipping a fair coin 2 times, and each landing on heads?

Let's look at this on a tree diagram...

Working with Tree Diagrams STEP 1: Write each individual probability on the appropriate branch.

STEP 2: To find the probability of a given outcome, multiply the probabilities along the branches.

STEP 3: If asked to find the probability of more than one “branch”, add your probabilities together.

Example: Consider two archers firing simultaneously at a target. Li has a 3/4 chance of hitting a target and

Yuka has a 4/5 chance of hitting a target. The tree diagram for this information is given below.

Lesson 10-8: Tree Diagrams Learning Goals:

#9: How do we use tree diagrams and probability rules to determine the probability of combined events?


IB QUESTIONS

RECALL: Two events are independent events when the occurrence of one event does not affect the

occurrence of the other.

RECALL: Two events are dependent events when the occurrence of one event does affect the

occurrence of the other.

We Try! Practice with Independent Events

1) A teacher has a box containing six type A calculators and four type B calculators.

The probability that a type A calculator is faulty is 0.1 and the probability that a type B calculator is faulty is 0.12.

(a) Complete the tree diagram given below, showing all the probabilities.

FAULTY

NOT FAULTY

FAULTY

NOT FAULTY

0.1

type A

type B

0.6

0.4

(b) A calculator is selected at random from the box. Find the probability that the calculator is

(i) a faulty type A;

(ii) not faulty;


0.65

not

red

red

red

notred

red

notred

You Try! Practice with Independent Events 2) Jim drives to work each day through two sets of traffic lights. The probability of the first set of traffic

lights being red is 0.65. If the first set is red then the probability that the next set of traffic lights is red is 0.46. If the first set is not red, the probability that the next set is red is 0.72.

a) Complete the tree diagram above.

b) Calculate the probability that i. the second set of traffic lights is red

ii. both traffic lights are red

iii. a traffic light is not red


Red

Green

Red

Green

Red

Green

25

24

We Try! Practice with Dependent Events 3) A bag contains two red sweets and three green sweets. Jacques takes one sweet from the bag, notes its

colour, then eats it. He then takes another sweet from the bag.

a) Complete the tree diagram below to show all probabilities.

b) Find the probability of i. drawing a red sweet.

ii. not drawing a red sweet.

iii. drawing red and then a green sweet.

iv. drawing a red and a green sweet.

v. both sweets being green

vi. both sweets being the same colour.


You Try! Practice with Dependent Events

4) There is a biscuit tin on a shelf. The tin contains one chocolate biscuit and nine plain biscuits.

A child chooses a biscuit from the tin. The child eats the biscuit and chooses another one from the tin. The tree diagram below represents the possible outcomes for this event.

110

910

ab

C

C

C

P

P

P

(i) Write down the values of a and b.

(ii) Complete the tree diagram above to show all probabilities.

(iii) Find the probability that both biscuits are chocolate.

(iv) What is the probability that at least one of the biscuits is chocolate?


correct

correct

incorrect

correctincorrect

incorrect

2–5

35–

34–

24–

—

24–

Name_________________________________

Date: ____________

Lesson 10-8 Homework

1) Sandra is attempting an exam question. She has to choose two correct statements from a list of five. Below is a tree diagram showing Sandra’s possible choices. One of the probability values is missing.

(a) Fill in the missing probability value on the diagram.

(b) If Sandra makes two guesses, what is the probability that

i. she gets the first question incorrect and the second question correct?

ii. she gets both of them correct?

iii. she will get only one of them correct?


0.4 C

C

B

B

B

B

BiologyChemistry

2) The events B and C are dependent, where C is the event “a student takes Chemistry”, and B is the event “a student takes Biology”. It is known that the probability a student takes Chemistry is 0.4. For students that take Chemistry the probability they take Biology is 0.6, otherwise the probability they take Biology is 0.5. a) Complete the following tree diagram.

b) Calculate the probability that a student does takes Chemistry but does not take Biology.

c) Calculate the probability that a student takes Biology.

3) Events A and B have probabilities P(A) = 0.4, P (B) = 0.38, and P(A B) = 0.54. a) Calculate P(A B).

b) State with a reason whether events A and B are independent.


4) The table below shows the number of left and right handed tennis players in a sample of 50 males and females.

Left handed Right handed Total

Male 3 29 32

Female 2 16 18

Total 5 45 50

If a tennis player was selected at random from the group, find the probability that the player is

(a) male and left handed;

(b) right handed;

(c) right handed or female.

5) A container holds 3 red, 4 blue, and 7 white marbles. A marble is chosen at random from the

container and is not replaced. A second ball is then chosen. Find the probability that

(a) the picks are both white

(b) the first pick is white and the second is red

(c) both picks are not red

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