STATISTICS & PROBABILITY

Course Overview

• Quarter: 3

Course Requirements

• Assessment Report Card
• Scientific Calculator
• Cattleya Notebook
  • Front: Quizzes and Activities
  • Back: Lecture notes
• Class Sections:
  • STEM 11 - Simon: blue
  • STEM 11 - Haggai: pink
  • STEM 11 - Saul: green
  • STEM 11 - Hazael: red
  • STEM 11 - Solomon: violet
  • STEM 11 - Hannah: yellow
  • STEM 11 - Samuel: orange
  • STEM 11 - Shadrach: black

Assessment Report Card

• Details:
  • Name: [Student Name]
  • School: My Messiah School of Cavite
  • School Year: 2025-2026
  • Grade & Section: Grade 11 Shadrach
  • Subject: Statistics & Probability
  • Adviser: Mr. Mikko Macapagal
• Quizzes, Activities, Recitations, Examinations:
  • Grades Tracking:
  • Quizzes (1-7)
  • Activities (1-7)
  • Recitations (1-10)
  • Examinations: Prelim, Midterm, Prefinal, Final
• Teacher: Ina-Marie B. Madridano, LPT

Expected Quarterly Outputs

• Assessments:
  • Preliminary Examination
  • Midterm Examination
  • 5 Quizzes
  • 4 Activities
  • Quarterly Project

Grading System

• Weights:
  • Written Work: 25%
  • Performance Tasks: 50%
  • Quarterly Assessment: 25%
• Components:
  • Quizzes
  • Prelim Exam
  • Pre-Final Exam
  • Individual Activity
  • Group Activity
  • Recitation
  • Project
  • Midterm Exam
  • Final Exam

Class Rules

• Attendance:
  • Late Entry: 5 minutes late results in NO ENTRY, applicable for first class or after break time.
• Use of Cellphones:
  • Cellphone usage as a calculator is prohibited.
• Participation:
  • Students must raise their hand to answer questions.

Recitation Policy

• Collected recitations will contribute to the score of the quarterly exam (midterm/final).
• Students achieving 10 recitations are exempt from the 2nd long test exam (pre-final).

UNDERSTANDING PROBABILITY

Week 1 Overview

What is Probability?

• Definition:
  • Probability is a field of mathematics that deals with chance.

Key Concepts in Probability

Experiment

• Definition:
  • An experiment is an activity in which the results cannot be predicted with certainty. Each repetition of an experiment is called a trial.

Outcome

• Definition:
  • An outcome is a result of an experiment.
• Event Definition:
  • An event is any collection of outcomes.

Sample Space

• Definition:
  • The sample space for a given experiment is a set $S$ that contains all possible outcomes of the experiment.
• Use in Probability Calculation:
  • For any experiment where the sample space is $S$, the probability of an event occurring is given by:
    $P(event) = \frac{n<em>{event}}{n</em>{sample \, space}}$
  • $n_{event}$: number of outcomes of the event
  • $n_{sample \, space}$: number of all possible outcomes

Example of Sample Space

• Experiment: Throwing a die
• Sample Space:
  $Sample \, Space = {1, 2, 3, 4, 5, 6}$

Probability Formula

• Formula Representation:
  $P(event) = \frac{n<em>{event}}{n</em>{sample \, space}}$

Practical Examples

Example 1: Tossing a Coin

• Sample Space:

  • A coin is tossed, find:
  • Answer:
    $Sample \, Space = {head, tail}$

• Probability Calculation:

  • Find Probability of Getting a Head:
    $P(head) = \frac{n<em>{head}}{n</em>{sample \, space}}$
  • Result Calculation:
    $P(head) = \frac{1}{2}$

Example 2: Standard Deck of Cards

• Example Question:
  • What is the probability of:
  • a. Picking a black card?
  • Calculation:$P(black) = \frac{n<em>{black \, cards}}{n</em>{sample \, space}}$
    • Details: A standard deck has 52 cards, with 26 being black.
    • Result:
      $P(black) = \frac{26}{52} = \frac{1}{2}$
• b. Picking a face card (king, queen, or jack)?
  • Calculation:
    $P(face) = \frac{n<em>{face \, cards}}{n</em>{sample \, space}}$
  • Result: Each suit has 3 face cards, giving total face cards across 4 suits as 12:
    $P(face) = \frac{12}{52} = \frac{3}{13}$
• c. Not picking a face card:
  • Calculation:
    $P(not \, face) = \frac{n<em>{not \, face \, cards}}{n</em>{sample \, space}}$
  • Result: 40 non-face cards:
    $P(not \, face) = \frac{40}{52} = \frac{10}{13}$

Example 3: Rolling a Die

• Questions:
  • a. Probability of rolling a 3:
    $P(3) = \frac{n<em>{3}}{n</em>{sample \, space}}$
  • b. Probability of rolling an even number:
    $P(even) = \frac{n<em>{even \, numbers}}{n</em>{sample \, space}}$
  • c. Probability of rolling a zero:
    $P(zero) = \frac{n<em>{zero}}{n</em>{sample \, space}}$

Practice Problems

• Problem 1: In my jar I have 5 balls. What is the probability of selecting a green ball?
• Problem 2: In my jar I have 6 balls. What is the probability of selecting a red ball?
• Problem 3: In my jar I have 7 balls. What is the probability of selecting a yellow ball?
• Problem 4: In my jar I have 9 balls. What is the probability of selecting a yellow or an orange ball?
• Problem 5: In my jar I have 8 balls. What is the probability of not selecting a red ball?

Conclusion

• Final Slide: Thank you for participating! Any questions?