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Probability Basics for 11th Grade

The document provides an introduction to probability and statistics concepts for 11th grade students. It defines probability as the likelihood of an event occurring based on the number of possible outcomes. It distinguishes between discrete and continuous random variables. Discrete variables have a finite number of possible values, while continuous variables can take on any value in an interval. Examples of each type of random variable are provided. The document also gives examples of calculating probabilities of events using concepts like sample space and counting favorable outcomes. It concludes with practice problems calculating probabilities for scenarios involving balls in bags and transportation methods based on surveys.

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Joseph Von Ryan
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41 views18 pages

Probability Basics for 11th Grade

The document provides an introduction to probability and statistics concepts for 11th grade students. It defines probability as the likelihood of an event occurring based on the number of possible outcomes. It distinguishes between discrete and continuous random variables. Discrete variables have a finite number of possible values, while continuous variables can take on any value in an interval. Examples of each type of random variable are provided. The document also gives examples of calculating probabilities of events using concepts like sample space and counting favorable outcomes. It concludes with practice problems calculating probabilities for scenarios involving balls in bags and transportation methods based on surveys.

Uploaded by

Joseph Von Ryan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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11TH GRADE

INTRODUCTION TO
PROBABILITY

STATISTICS AND PROBABILITY


2ND SEM LESSON 1
LESSON’S OBJECTIVES
● Recall the definition of Probability of occurrence of
event.
● Illustrates a random variable (discrete and continuous)
● Distinguishes between a discrete and a continuous
random variable
What is Probability?
If 100 students will participate in a raffle game,
what is the chance of winning the prize?

Probability is the extent to which the event is


likely to occur, measured by:

𝑁𝑜.𝑜𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑒𝑣𝑒𝑛𝑡 𝐴 𝑛(𝐴)


𝑃 𝐴 = = 𝑛(𝑆)
𝑁𝑜.𝑜𝑓 𝑎𝑙𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Random Variable
A random variable is called
discrete if it has either a finite or a countable
number of possible values. Thus, a
discrete random variable X has possible values
x1,x2, x3,....

A random variable
is called continuous if its possible values
contain a whole interval of numbers.

.
Discrete Random Variable
Example:
Discrete Random Variable
1. Number of heads in 4 flips of a coin
(possible outcomes are 0, 1, 2, 3, 4)
2. Number of classes missed from March 2020
to December 2020
3. The number of siblings a person has
4. The number of Covid-19 cases in Negros
Oriental in 2020
5. The number of students involve in Online
classes in Neg Or Division
during this pandemic time
.
Continuous Random Variable
Example:
Continuous Random Variables
1. Heights of students in class
2. Time to finish a module
3. Hours spent exercising
4. Distance travelled from Dumaguete to
Pamplona.
Example 1
Suppose you tossed 3 coins, these are the list of all
possible outcomes.
LIST OF ALL OUTCOMES
HHH HTT

HHT THT

HTH TTH

THH TTT

Consider the Event A of Getting 2 heads and 1 tails.

Probability of getting 2 heads and 1 tail is


3
𝑃 𝐴 = 𝑃 2𝐻1𝑇 =
8
Example 2
Suppose you tossed 3 coins, these are the list of all
possible outcomes.
LIST OF ALL OUTCOMES
HHH HTT

HHT THT

HTH TTH

THH TTT

Consider the Event B of getting exactly 1 head.

Probability of getting exactly 1 H


3
𝑃 𝐵 = 𝑃 1𝐻 =
8
Example 3
Suppose you tossed 3 coins, these are the list of all
possible outcomes.
LIST OF ALL OUTCOMES
HHH HTT

HHT THT

HTH TTH

THH TTT

Consider the Event C getting exactly 3 Tails

Probability of getting exactly 3 T


1
𝑃 𝐶 = 𝑃 3𝑇 =
8
Example 4
Suppose you roll a Fair Die? These are all the possible
outcomes
LIST OF ALL OUTCOMES
1 2

3 4

5 6

Consider the Event S of getting EVEN NUMBERS.

Probability of getting Even numbers is


3 1
𝑃 𝑆 = 𝑃 𝐸𝑉𝐸𝑁 = =
6 2
Let’s Practice few
Examples
TRY THIS!!!
A bag contains 7 white balls and 11 orange balls.
If the ball is drawn at random from the bag, find the Probability that the
ball is:
Probability of getting Green
1. Green. 0
𝑃 𝐺 = =0
2. White.
18

3. Not White.
TRY THIS!!!
A bag contains 7 white balls and 11 orange balls.
If the ball is drawn at random from the bag, find the Probability that the
ball is:
Probability of getting White
1. Green. 7
𝑃 𝑊 =
2. White. 18
3. Not White.
TRY THIS!!!
A bag contains 7 white balls and 11 orange balls.
If the ball is drawn at random from the bag, find the Probability that the
ball is:
Probability of getting Not White
1. Green. 11
𝑃 𝑌 =
2. White. 18
3. Not White.
Activity No. 1
1. Assuming you are tossing a fair die. What is the
Sample Space?
Find the Probability of getting:
a. An odd number
b. A number greater than or equal to 3
c. A number less than 6
d. An even number
Activity No. 1
2. Suppose a box of Marbles has the following
colors. 6 Red marbles, 5 Black Marbles, 2 Blue
Marbles, and 2 White Marbles. Find the
probability of getting:
a. White Marble.
b. Red Marble
c. Yellow Marble
d. Blue Marble
Activity No. 1
3. After a certain survey with total of 100
people around Sapang Palay, there 23 person
who commute when going to work, 11 person
use Private automobile and 17 people use E-
bike as transportation. What is the Probability
that the person interviewed use:
a. Commuter c. Private Automobile
b. E-bike d. Not E-bike user
Thank you for
listening!!
Do you have any
question??

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