PROBABILITY OF A SIMPLE EVENT

W7

Learning Area

Mathematics

Grade Level

8

Quarter

4th

Date

I. LESSON TITLE

PROBABILITY OF A SIMPLE EVENT

II. MOST ESSENTIAL LEARNING

COMPETENCIES (MELCs)

Finds the probability of a simple event (M8GE-IVh-1)

III. CONTENT/CORE CONTENT

Probability

IV. LEARNING PHASES AND LEARNING ACTIVITIES I. Introduction (Time Frame: 20 minutes)

Hi there, Grade 8 students! For today, we will talk about the probability of a simple event. Again, let us recall, the probability is a measure or estimation of how likely it is that an event will occur. It can be expressed as a fraction, a decimal, or a percent.

Review of the past lesson:

In flipping a coin, there are 2 possible outcomes, the head and the tail.

Therefore, the probability of getting a head is 1/2, while the probability of getting a tail is also 1/2. Try this activity.

Activity 1. “Let’s Roll It On” (Note: A die has 6 faces)

When a fair die is thrown, what is the probability of getting a. the number 4?

b. an odd number? c. a number that is more than 6?

d. a number that is less than 7? D. Development (Time Frame: 60 minutes)

PROBABILITY OF A SIMPLE EVENT

The Probability of an event, P(event), is a number from 0 to 1, which tells how likely an event is to happen. The more likely an event is to occur, the higher its probability. The less likely an event is to occur, the lower its probability.

Remember:

• The probability of any event is a number (either a fraction, a decimal or a percent) from 0 to 1. • The sum of the probabilities of all outcomes in the sample space is 1.

• If an event will never happen, then the probability is 0. • If an event is sure to happen, then the probability is 1

One of the best examples of this is the weather today. By browsing your weather app on your mobile phone, you may know if there is a chance of rain today. Based on its given data, which is presented in either decimal, fraction, or percent, you may conclude if it is likely to rain, unlikely to rain, surely to rain, or it will not rain.

Probability of Simple Events

An event consisting of a single point of the sample space is known as a simple

event. To solve the probability of a simple event, we need to get the ratio of

favorable outcomes to the total number of possible outcomes or known

as the Sample Space. It is being shown by the formula below: P(event)= Number of favorable outcomes,

Number of all outcomes Activ ity 1 an sw er k ey: a. ! " b. # " or ! $ 0 c. d. 1

Head

(H)

Tail (T)

=

Find the probability of the following events:

1. When a fair die is thrown, what is the probability of getting a. the number 4 Answer: P(4) = #

$ b. an odd number Answer: P(odd) = #

%

c. a number that is more than 6 Answer: P(more than 6) = 0 d. a number that is less than 7 Answer: P(less than 7) = 1 SOLUTIONS:

a. Event of getting a number 4.

4 occurs only once, that is why the number of favorable outcomes is 1. There are 6 possible outcomes in a die, {1, 2, 3, 4, 5, 6}. P(event)= Number of favorable outcomes,

Number of all outcomes

, by substituting the values of n and N, we have P(4) =𝟏 𝟔

b. Event of getting an odd number.

The odd numbers from 1 to 6 are 1, 3, 5, so there are 3 favorable outcomes. There are 6 possible outcomes in a fair die, {1, 2, 3, 4, 5, 6}.

P(odd) = (

$ (reduce the fraction in lowest term) P(odd) = 𝟏

𝟐

c. Event of getting a number that is more than 6

There is no number more than 6 in a die, so 0 is the favorable outcome. Since a fair die has 6 possible outcomes {1, 2, 3, 4, 5, 6}, then

P(more than 6) = *

$ (Zero divided by any number is always zero. P(more than 6) = 0. A probability of 0 means the event will never occur.

d. Event of getting a number that is less than 7

There are 6 numbers less than 7, these are {1, 2, 3, 4, 5, 6}, while there are 6 possible outcomes {1, 2, 3, 4, 5, 6}. P(less than 7) =$

$ (simplify the answer)

P(less than 7) = 1. A probability of 1 means the event will always occur.

2. In a Grade 8 class in Prudencia D. Fule Memorial National High School, the math teacher writes each letter of the word MATHEMATICS on a card. A card is chosen at random from the box. What is the probability of getting the letter ‘M’? SOLUTION:

Since the card is randomly selected, it means that each card has the same chance of being selected. There are 11 letters in the box {M1, A, T, H, E, M2, A, T, I, C, S} and there are two cards with the letter ‘M’ {M 1, M 2}.

Using the formula,

P(E) = ! " P(E) =! " P(E) = ! " P(E) = ! "

IV. LEARNING PHASES AND LEARNING ACTIVITIES P(M) = 𝟐

𝟏𝟏 , the probability of getting the letter M is 𝟐

𝟏𝟏 or 0.18 or 18%.

3. In the celebration of the International Day of Mathematics, Del Remedio National High School conducted a Poster Making Contest among its students. If there are 12 male participants and 18 female participants, what is the probability that the winner is a:

a. male student? b. female student?

SOLUTION:

• To get the probability of a male winner, get the ratio of the number of male students to the total number of students. So, we have:

Given: Solution and answer:

n = 12 (number of occurrences) N = 30 (total number of outcomes)

Therefore, the probability of a male winner is 𝟐

𝟓 which can also be expressed in decimal as 0.4, and in percentage as 40%.

• To solve for the probability of a female winner, we may use the same method in getting the probability of the male winner. So, we have:

Given: Solution and answer:

n = 18 (number of occurrences) N = 30 (total number of outcomes)

Therefore, the probability of a female winner is 𝟑

𝟓 which can also be expressed in decimal as 0.6, and in percentage as 60%. E. Engagement (Time Frame: 40 minutes)

Learning Task 1. “Ball is Life”

A box has 10 balls. Each ball is marked with single digit from 0 to 9. One ball is randomly selected. What is the probability that the number is:

1. greater than 6? 2. less than or equal to 3? 3. odd?

4. not 0? 5. 3 or 9?

Learning Task 2. “Fruit Panda”

There are 4 rambutan, 5 lanzones, 1 pineapple, and 2 mangoes in a basket. Suppose you select one fruit at random. Find each probability. 1. P(mangoes) 2. P(rambutan) 3. P(rambutan or mango) 4. P(not pineapple) 5. P(not banana)

(These are the 3 representations of answers; fraction, decimal and percent)

https://everywhere.idm314.org/. P(male winner) = -.

=

=

= 0.4 = 40%

%40%

=

=

IV. LEARNING PHASES AND LEARNING ACTIVITIES A. Assimilation (Time Frame: 20 minutes)

“Problem No More”

Find the probability of the following events:

1. If a letter is chosen at random from the word PROBABILITY, find the probability that the letter chosen is: a. a vowel

b. a consonant

2. A frontliner will be chosen from a certain group. There are 9 nurses and 8 doctors in that group. What is the probability that the chosen frontliner is a doctor?

3. A card is drawn in a standard deck of cards. Find the probability that the card drawn is a queen?

4. Grade 8 Math teacher of San Pablo City Integrated High School picks a student at random in his class. If there are 15 males and 22 females in the class, what is the probability that a female student will be picked?

V. ASSESSMENT (Time Frame: 20 minutes)

QUIZ: Direction: Choose the letter of the correct answer

1. What is the probability of getting the number 5 when a fair die is thrown? A. 0 B. 1/6 C. 1/2 D. 1

2. When a fair die is thrown, what is the probability of getting an even number? A. 0 B. 1/6 C. 1/2 D. 1

3. In a standard deck of cards, what is the probability of getting a queen card? A. 1/52 B. 1/25 C. 1/13 D. 0

4. Find the probability that the letter is “consonant” if a letter is to be selected from the word FILIPINO? A. 1 B. 1/2 C. 3/8 D. 1/8

5. In a school-based virtual quiz bee at San Pablo City Integrated High School, the winner will receive smart phone and mobile load as rewards that they can use for their online class. If there are 198 Grade 7 students, 200 Grade 8 students, 212 Grade 9 students, and 190 Grade 10 students in the school, what is the probability that the winner will be a grade 8 student?

A. 1/8 B. 1/4 C. 1/2 D. 1 VI. REFLECTION (Time Frame: 10 minutes)

• Communicate your personal assessment as indicated in the Learner’s Assessment Card. Personal Assessment on Learner’s Level of Performance

Using the symbols below, choose one which best describes your experience in working on each given task. Draw it in the column for Level of Performance (LP). Be guided by the descriptions below:

¶ - I was able to do/perform the task without any difficulty. The task helped me in understanding the target content/ lesson. ü - I was able to do/perform the task. It was quite challenging, but it still helped me in understanding the target content/lesson.

? – I was not able to do/perform the task. It was extremely difficult. I need additional enrichment activities to be able to do/perform this

task.

Learning Task LP Learning Task LP Learning Task LP Learning Task LP

Number 1 Number 3 Number 5 Number 7

Number 2 Number 4 Number 6 Number 8

VII. REFERENCES • Mathematics 8 Learner’s Module pages 562 – 571

• https://byjus.com/maths/types-of-events-in-probability/#Simple-Events

• https://www.cliffsnotes.com/study-guides/statistics/probability/probability-of-simple-events

•

Prepared by: BENEDICK R. LALUZ

Master Teacher 1, Mathematics Checked by: MA. FILIPINA M. DRIO LAILA R. MALOLES HENRY P. CONTEMPLACION MARIA TERESA J. MACATANGAY