Topicm97eab31bc6ccaa3f_1528449000663_0Topic

Calculating probability of experiments

Levelm97eab31bc6ccaa3f_1528449084556_0Level

Third

Core curriculumm97eab31bc6ccaa3f_1528449076687_0Core curriculum

XII. Theory or probabilityprobabilityprobability and statistics.

Basic level. The student:

1) calculates probability using the classical model.

Timingm97eab31bc6ccaa3f_1528449068082_0Timing

45 minutes

General objectivem97eab31bc6ccaa3f_1528449523725_0General objective

Choosing and creating mathematical models to solve practical and theoretical problems.

Specific objectivesm97eab31bc6ccaa3f_1528449552113_0Specific objectives

1. Calculating probability using the classical model.

2. Calculating probability of two‑stage experiments using the probability tree diagrams.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm97eab31bc6ccaa3f_1528450430307_0Learning outcomes

The student:

- calculates probability using the classical model,

- calculates probability of two‑stage experiments using the probability tree diagrams.

Methodsm97eab31bc6ccaa3f_1528449534267_0Methods

1. Situational analysis.

2. JIGSAW.

Forms of workm97eab31bc6ccaa3f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm97eab31bc6ccaa3f_1528450127855_0Introduction

Students revise information about probabilityprobabilityprobability they learnt during the previous lesson.

Procedurem97eab31bc6ccaa3f_1528446435040_0Procedure

Students do exercises by applying learned method.

Task 1

Draw one number from the set of two‑digit numbers made of digits {3, 5, 7}. Write elements of the sample space of elementary events Ω, knowing that digits can be repeated. Calculate the probability of drawing a number greater than 55.

Students work individually, using computers. Their task is to get to know the  interactive illustration, describing the tree diagram methodtree diagram methodtree diagram method.

There are three blue cardboard pieces and two yellow cardboard pieces on the table. Next to them, there are two boxes. In box A, there is one blue piece and in box B, there is one yellow and four blue pieces. If we take a blue piece from the table, we draw from box A, if yellow – from box B. What is the probability of an event A – that we get two pieces in the same colour?

[Interactive graphics]

$P\left(A\right)=\frac{3}{5}·\frac{1}{2}+\frac{2}{5}·\frac{1}{5}=\frac{3}{10}+\frac{2}{25}=\frac{30}{100}+\frac{8}{100}=\frac{38}{100}=0,38$

Probability of the event A is 0,38.

After having completed the exercise, students present results of their observations:

To calculate the probability using the tree diagram method:

1. We present outcomes of the experiments using the tree
2. We write the probability of choosing each option on each stage of the experiment on separate
branches
3. We mark branches favourable to the description of an event
4. We calculate the product of probabilities of events from each stages of marked branches
5. We calculate the sum of obtained productsm97eab31bc6ccaa3f_1527752263647_0To calculate the probability using the tree diagram method:

1. We present outcomes of the experiments using the tree
2. We write the probability of choosing each option on each stage of the experiment on separate
branches
3. We mark branches favourable to the description of an event
4. We calculate the product of probabilities of events from each stages of marked branches
5. We calculate the sum of obtained products

Students do the task presented in the beginning of the lesson, this time using the tree diagram method. They compare obtained results.

The teacher divides students into 4 persons groups that work using the JIGSAW method. Each member of the group gets different task from the tasks below. After solving the tasks, students gather in groups that were doing the same task. They discuss the solutions and clarify any doubts. Then, they return to the initial groups and present the solutions to other members.

Task 2

Do the exercise using the classical definition of probabilityprobabilityprobability.

We roll a symmetric, six‑sided dice two times. Calculate the probability of getting a number not smaller than 4 both times.

Task 3

Do the exercise using the tree diagram method.m97eab31bc6ccaa3f_1527752256679_0Do the exercise using the tree diagram method.

We roll a symmetric, six‑sided dice two times. Calculate the probability of getting a number not smaller than 4 both times.m97eab31bc6ccaa3f_1527752256679_0We roll a symmetric, six‑sided dice two times. Calculate the probability of getting a number not smaller than 4 both times.

Task 4

Do the exercise using the tree diagram method.

There are five blue beads and two golden beads in a sack. We take out two beads and do not put them back. Calculate the probability of taking out two beads of the same colour.

Task 5

Do the exercise using the tree diagram methodtree diagram methodtree diagram method.

While flipping a non‑symmetric coin, the probabilityprobabilityprobability of getting heads is equal to $\frac{{\displaystyle 2}}{3}$, and tails $\frac{{\displaystyle 1}}{3}$. Calculate the probability of getting at least one heads in two trials.

The teacher evaluates students’ work and clarifies doubts.

An extra task:

There were three times less winning tickets than empty tickets in the box, during the lottery. The probabilityprobabilityprobability of getting one winning ticket and one empty ticket is $\frac{{\displaystyle 45}}{119}$. How many winning and empty tickets are there in the box?

Lesson summarym97eab31bc6ccaa3f_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

To calculate the probability using the tree diagram method:

1. We present outcomes of the experiments using the tree,
2. We write the probability of choosing each option on each stage of the experiment on separate
branches,
3. We mark branches favourable to the description of an event,
4. We calculate the product of probabilities of events from each stages of marked branches,
5. We calculate the sum of obtained products.m97eab31bc6ccaa3f_1527752263647_0To calculate the probability using the tree diagram method:

1. We present outcomes of the experiments using the tree,
2. We write the probability of choosing each option on each stage of the experiment on separate
branches,
3. We mark branches favourable to the description of an event,
4. We calculate the product of probabilities of events from each stages of marked branches,
5. We calculate the sum of obtained products.

Selected words and expressions used in the lesson plan

experimentexperimentexperiment

probabilityprobabilityprobability

product of probabilities of events from each stageproduct of probabilities of events from each stageproduct of probabilities of events from each stage

tree diagram methodtree diagram methodtree diagram method

two‑stage experimenttwo‑stage experimenttwo‑stage experiment