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MATHEMATICS TEACHER 9 GRADE

MR. DEDI

Learning Instructions

(Langkah-langkah umum cara belajar secara mandiri atau bersama disekolah yang harus dipahami oleh siswa)

• Awali kegiatan belajar dengan berdoa.

• Silakan mempelajari Learning Materials terlebih dahulu untuk mendapat pemahaman yang baik terkait topik/ materi yang akan dipelajari.

• Setelah mendapat pengalaman belajar dan memahami topik/materi dengan baik silakan lanjutkan ketahap Exercises. Apabila belum siap silakan mempelajari kembali Learning Materials atau bertanya kepada guru melalui WA / memanfaatkan link Ask To Chat GPT yang tersedia. 

Note : Jangan belajar sekedarnya, ikutilah  petujuk belajar di atas untuk mendapat hasil yang lebih maksimal.

MATHEMATICS MATERIAL GRADE IX  OPPORTUNITY (PROBABILITY)

A. Definition of Opportunity

Chance is the probability of an event occurring.

In everyday life, odds are used to estimate the likelihood of an event, such as the chance of rain, the chance of winning a game, or the chance of passing a test.

B. Terms in Opportunity

1. Experiment: Activities that are carried out to obtain certain results.

   Example: tossing a coin or dice.

2. Sample Room(s): A set of all possible outcomes.

   Example: Roll one die → S = {1, 2, 3, 4, 5, 6}

3. Sample Point: Every member of the sample room.

4. Genesis (A): The subset of the sample space.

C. Opportunity Formula

The probability formula for an event is:

P(A) = n(A) / n(S)

Description:

- P(A) = chance of occurrence A

- n(A) = number of members of event A

- n(S) = number of members of the sample room

Odds value: 0 ≤ P(A) ≤ 1

If P(A) = 0 → impossible to occur

If P(A) = 1 → must occur

D. Sample Questions and Discussion

Example 1: A die is rolled once. Determine the chances of the number 4 appearing!

Answer:

S = {1,2,3,4,5,6} → n(S) = 6

A = {4} → n(A) = 1

P(A) = 1/6

Example 2: A coin is tossed once. Determine the chances of the image appearing!

S = {number, image} → n(S) = 2

A = {image} → n(A) = 1

P(A) = 1/2

Example 3: A die is rolled once. Determine the chances of even numbers!

A = {2,4,6} → n(A) = 3

n(S) = 6

P(A) = 3/6 = 1/2

E. Relative Frequency

Relative frequency is a comparison of the number of events that occur with the number of experiments. Formula: Relative Frequency = Frequency of events / Many experiments. The more experiments are performed, the relative frequency will get closer to the theoretical chance.

F. Complement Opportunities

A complement opportunity is a chance that an event will not occur.

Formula: P(Ac) = 1 - P(A)

Example: If the chance of passing the test is 0.8 then the chance of not passing is 1 - 0.8 = 0.2

G. Summary

1. Chance is the possibility of an event occurring.

2. Opportunity formula: P(A) = n(A) / n(S)

3. Value the odds between 0 and 1.

4. Complement opportunity: P(Ac) = 1 - P(A)

5. The frequency is relatively close to chance if the experiment is repeated repeatedly.

MATERI MATEMATIKA KELAS IX

PELUANG (PROBABILITY)

A. Pengertian Peluang

Peluang adalah kemungkinan terjadinya suatu kejadian.

Dalam kehidupan sehari-hari, peluang digunakan untuk memperkirakan kemungkinan suatu peristiwa, seperti peluang hujan, peluang menang dalam permainan, atau peluang lulus ujian.

B. Istilah-Istilah dalam Peluang

1. Percobaan: Kegiatan yang dilakukan untuk mendapatkan hasil tertentu.

   Contoh: melempar koin atau dadu.

2. Ruang Sampel (S): Himpunan semua hasil yang mungkin terjadi.

   Contoh: Melempar satu dadu → S = {1, 2, 3, 4, 5, 6}

3. Titik Sampel: Setiap anggota dari ruang sampel.

4. Kejadian (A): Himpunan bagian dari ruang sampel.

C. Rumus Peluang

Rumus peluang suatu kejadian adalah:

P(A) = n(A) / n(S)

Keterangan:

- P(A) = peluang kejadian A

- n(A) = banyaknya anggota kejadian A

- n(S) = banyaknya anggota ruang sampel

Nilai peluang: 0 ≤ P(A) ≤ 1

Jika P(A) = 0 → mustahil terjadi

Jika P(A) = 1 → pasti terjadi

D. Contoh Soal dan Pembahasan

Contoh 1: Sebuah dadu dilempar sekali. Tentukan peluang muncul angka 4!

Jawab:

S = {1,2,3,4,5,6} → n(S) = 6

A = {4} → n(A) = 1

P(A) = 1/6

Contoh 2: Sebuah koin dilempar sekali. Tentukan peluang muncul gambar!

S = {angka, gambar} → n(S) = 2

A = {gambar} → n(A) = 1

P(A) = 1/2

Contoh 3: Sebuah dadu dilempar sekali. Tentukan peluang muncul angka genap!

A = {2,4,6} → n(A) = 3

n(S) = 6

P(A) = 3/6 = 1/2

E. Frekuensi Relatif

Frekuensi relatif adalah perbandingan banyaknya kejadian yang terjadi dengan banyaknya percobaan.
Rumus: Frekuensi Relatif = Frekuensi kejadian / Banyak percobaan.
Semakin banyak percobaan dilakukan, frekuensi relatif akan semakin mendekati peluang teoritis.

F. Peluang Komplemen

Peluang komplemen adalah peluang tidak terjadinya suatu kejadian.

Rumus: P(Ac) = 1 - P(A)

Contoh: Jika peluang lulus ujian adalah 0,8 maka peluang tidak lulus adalah 1 - 0,8 = 0,2

G. Rangkuman

1. Peluang adalah kemungkinan terjadinya suatu kejadian.

2. Rumus peluang: P(A) = n(A) / n(S)

3. Nilai peluang antara 0 dan 1.

4. Peluang komplemen: P(Ac) = 1 - P(A)

5. Frekuensi relatif mendekati peluang jika percobaan dilakukan berulang kali.

Video

Exercises

(Exercises merupakan latihan soal yang dikerjakan setelah belajar mandiri) 

1. Two Dice Problem

Two six-sided dice are rolled at the same time.
What is the probability that the sum of the numbers is greater than 9?

2. Two Coins

Two coins are tossed at the same time.
What is the probability of getting exactly one tail?

3. Colored Balls Without Replacement

A box contains 6 red balls, 4 blue balls, and 5 green balls.
Two balls are chosen one after another without replacement.
What is the probability that both balls are blue?

4. Cards Greater Than 7

Cards numbered 1 to 12 are placed in a box. Two cards are picked at random without replacement.
What is the probability that both cards show numbers greater than 7?

5. Student Committee Selection

There are 10 boys and 15 girls in a class.
Two students are chosen randomly to be class leaders.
What is the probability that both selected students are girls?

6. Multiple Conditions

A number is chosen randomly from 1 to 20.
What is the probability that the number is a multiple of 4 or a multiple of 5?

7. Mixed Marbles

A jar contains 8 white marbles, 6 black marbles, and 4 red marbles.
Two marbles are drawn without replacement.
What is the probability that one marble is white and the other is black?

8. At Least One Six

A die is rolled twice.
What is the probability of getting at least one six?

9. Letter Probability (Repeated Letters)

The letters of the word “PROBABILITY” are written on separate pieces of paper and placed in a box.
Two letters are chosen randomly without replacement.
What is the probability that both letters are vowels? tung tung tung sahur akan datang

10. Test Result Selection

In a school, 5O students passed and 3O students failed a science exam.
Two students are selected randomly.
What is the probability that one student passed and the other failed?