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WorksheetsGENERAL KNOWLEGE (STATISTICS AND PROBABILITY)
Total questions: 160
Worksheet time: 6hrs 38mins
It is a numerical quantity that is assigned to the outcome of an experiment.
Statistics
Probability
Random Variable
Distribution
It is the set of all possible outcomes in an experiment.
Random Variable
Sample Space
Mean
Data
Two coins are tossed in an experiment. Which of the following list is the sample space?
S= {HH, HT, TH, TT}
S= {HH, TT}
S= { HT, TH, TT}
S= {HH, HT, TT}
Supposed two coins are tossed consecutively and we are interested in the number of heads that will come out. Determine the values of the random variable H (number of heads).
0,2,3,4
0,1,2,3
0,1,2
0,1,2,3,4
Nico label an x- axis with points earned and the corresponding y - axis with the number of players. He plot one against the other and he obtain a bar graph called a what?
(a)
If you had no idea what the answer to this four option multiple choice was and took a wild guess, what is the probability that you are correct?
(a)
Which of the following are the properties of a Normal Probability Distribution.
The distribution curve is bell - shaped.
The curve is symmetric about its center, the mean.
The mean, the median, and the mode coincide at the center.
The area under the curve is 1 or 100%
The tails of the curve is asymptotic to the base line.
TRUE or FALSE: The standard normal distribution of a random variable is a normal distribution with mean =0 and standard deviation =1.
TRUE
FALSE
TRUE or FALSE: The area between 0 and a positive value z is the same as the area between 0 and -z.
TRUE
FALSE
TRUE or FALSE: The area that corresponds to z = 2.58 is the same as the area that corresponds to z = -2.58, which is A = 0.4951
TRUE
FALSE
Find the area that corresponds to z = -1.15
(a)
What is the probability that the value of a standard normal random variable z lies between 0 and 1.28?
(a)
It is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.
(a)
It is a variable whose value is determined by the outcome of a random experiment.
(a)
It is a random variable whose set of assumed values that is countable.
(a)
A random variable whose set of assumed values that is uncountable, usually arises from measurement.
(a)
It is a number which describes the spread of the distribution.
(a)
The following table represents the probability distribution X, the employment status of adults in a city.
What is the probability that the adults isn't retired?
(a)
If you select one adult at a random from this community, what is the probability that the adults is employed as part -time?
(a)
If you select one adult at a random from this community, what is the probability that the adults is working either part - time or full - time?
(a)
A coin is tossed three times. How many total outcomes are possible?
4
8
16
36
How many outcomes are there with tossing a coin and rolling a die?
2
6
12
24
Which shows the sample space for flipping two coins?
S = {H, T}
S = {HH, TT}
S = {HH, HT, TT}
S = {HH, HT, TH, TT}
A function whose value is a real number determined by each elements?
Random Variable
Sample Space
Continuous
Discrete
A couple has four children, let X be the random variables. What are the possible random variable of X?
X = {boy, girl}
X = {0, 1, 2, 3}
X = {0, 1, 2, 3, 4}
X = {0, 1, 2, 3, 4, 5, 6}
A random variable that can take on a finite or countable number of distinct values?
Discrete
Continuous
sample space
random variable
List the sample space for this experiment: A coin is tossed at the start of a basketball match.
S = {HH, TH, HT, TT}
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
S = {H, T}
S = {HH, TT}
Which of the following random variable is continuous?
The speed of bus
The number of female students
The number defective mobile phone
Choosing a natural number less than 100
Flipping a pair of a coin, let X the number of heads in four flips of a coin?
X = {0, 1, 2, 3}
X = {1, 2, 3}
X = {0, 1, 2}
X = {1, 2}
Which of the following random variable is discrete?
The time needed to finish the module
The amount of sugar in a cup of coffee
A room temperatures in a certain time of a day
Tallying the number of COVID cases in the municipality
Set of integers, where the integers from 2 to 6. What are the possible random variable of integers?
Z = {2, 4, 6}
Z = { 2, 3, 4. 5, 6}
Z = {3, 5, 6}
Z = { 3, 5}
Which of the following variables can assume only an infinite number or measurable?
Discrete
Continuous
Discrete Probability Distribution
Random variables
What is the term used for the set of all possible outcomes in an experiment?
Discrete
Continuous
Sample space
Random variables
A two coins are tossed, which is NOT a possible value of the random variable for the number of heads?
0
1
2
3
Which of the following is discrete random variable?
John weighs 65 kg
John is 160 cm tall
John has two sisters
John ran 200 meters in 15.5 seconds
These kind of observations are made using instruments such as rulers, balances and thermometers.
qualitative
quantitative
These kind of observation use your senses to observe results.
qualitative
quantitative
Probability is...
the likelihood of the occurrence of an event
the name given to any controlled and repeatable process
a set of possible outcomes resulting from a particular experiment
a single specific possible result of an experiment
An Event is...
the likelihood of the occurrence of an event
the name given to any controlled and repeatable process
a set of possible outcomes resulting from a particular experiment
a single specific possible result of an experiment
An Outcome is...
the likelihood of the occurrence of an event
the name given to any controlled and repeatable process
a set of possible outcomes resulting from a particular experiment
a single specific possible result of an experiment
An Experiment is...
the likelihood of the occurrence of an event
the name given to any controlled and repeatable process
a set of possible outcomes resulting from a particular experiment
a single specific possible result of an experiment
An Independent Event is...
the likelihood of the occurrence of an event
not affected by previous events
a set of possible outcomes resulting from a particular experiment
affected by previous events
An Dependent Event is...
the likelihood of the occurrence of an event
not affected by previous events
a set of possible outcomes resulting from a particular experiment
affected by previous events
Gwinnett County Public Schools randomly selected 230 teachers to find out which technology resource is the most effective. 30 teachers chose Safari Montage, 45 selected Learn Zillion, 100 chose Ed Puzzle, and 55 chose Kahoot. GCPS concluded that all teachers prefer Ed Puzzle.
It is a field of mathematics that deals with chances.
Probability
Algebra
Geometry
Trigonometry
It is the list of all possible outcomes in an experiment.
Experiment
Event
Sample Space
Outcome
It is a set whose elements are the numbers assigned to the outcomes of an experiment. It is denoted by a capital letter, usually 'X'
Outcome
Random Variable
Event
Sample Space
It is a random variable that can take on a finite (countable) number of distinct values.
Discrete Random Variable
Continuous Random Variable
Random Variable
Sample Space
What is the sample space in picking a card in a standard deck of cards?
2
6
36
52
A coin is tossed. Find the probability of getting a head?
21
41
43
1
What is the probability of picking a spade card in a standard deck of cards?
41
133
5223
521
A coin is tossed thrice. Let X be the random variable representing the number of heads that occur. What would be the values of the random variable X?
X={0,1,2}
X={0,1,2,3}
Y={0,1,2,3}
Y={1,2,3,4}
An athlete only takes 9 seconds to finish running the 100m sprint. What type of variable is given in this scenario?
Random Variable
Discrete Random Variable
Continuous Random Variable
Sample Space
Identify the type of variable: amount spent in pesos on food in one week.
Discrete Random Variable
Continuous Random Variable
Which of the following is a discrete probability distribution?
The average amount of electricity consumed
The number of patients in a hospital
The amount of paint used in repainting a building
The average weight of female athletes
If two coins are tossed, which is not a possible value of the random variable for the number of heads?
0
1
2
3
Which of the following is not a true statement?
The value of a random variable could be zero.
Random variables can only have one value.
The probability of the value of a random variable could be zero.
The sum of all the probabilities in a probability distribution is always equal to one.
It is a characteristic that can assume different values.
probability distribution
variable
discrete
nominal
It consist of the values of the random variable can assume and the corresponding probabilities.
Probability
Frequency Distribution
Probability Distribution
Distribution
Variables that are expressed as a whole and is countable.
Discrete
Continuous
Nominal
Ordinal
Which of the following best describes the continuous variable?
Expressed as a whole
Countable
weight
Uncountable
It is the list of all possible outcomes.
probability distribution
disctrete variable
possible outcomes
sample space
It is the most appearing number.
mean
mode
median
variance
Process of collecting, analyzing, interpreting and presenting data.
probability
statistics
variable
none of the above
Which statement about the medians is true?
Which statement about the data is NOT true?
Identify whether the experiment involves a discrete or a continuous random variable.
Rotating a spinner that has 4 equally divided parts: blue, green, yellow, and red
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Collecting data about the mileage per liter of a certain brand and model of a car
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
tossing a pair of fair coins
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Recording the number of points scored by a NBA team in each game of the 2018 season
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Number of phone calls answered by a call center agent during his/her shift
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Recording number of medals that the Philippine team won in each of the past 20 Olympic games
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Measuring the distance travelled by different cars using 1-liter of gasoline
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Measuring the length of time it takes before a dolphin surfaces in the ocean to breath
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Recording the number of times each student goes to the bathroom in each school day
Discrete Random Variable
Continuous Random Variable
Identify whether the experiment involves a discrete or a continuous random variable.
Tallying the number of times a student has been late during the 1st term
Discrete Random Variable
Continuous Random Variable
Is this a probability distribution?
No, the sum of p(x) does not equal 1.
Yes, all p(x) are between 0 and 1.
No, all p(x) are not between 0 and 1.
Yes, the sum p(x) is 1.
A discrete random variable X has the probability distributions shown in the table. Find the value of k.
1/3
7/12
1/12
1/4
A discrete random variable X has the probability distribution shown in the table. Find P(1 < X ≤ 3).
7/8
1/2
5/8
3/8
A discrete random variable X has the probability distribution shown in the table. Find P(X < 2).
7/8
1/2
5/8
3/8
A discrete random variable X has the probability distribution shown in the table. Find P(X > 3).
1
7/8
1/8
0
Let X be the number of heads obtained when tossing
a fair coin 3 times.
What are the possible values of X?
0,1,2,3,
1,2,3,
0,1,2,3,4
1,2,3,4
It is the set of all possible outcomes in an experiment.
Random Variable
Sample Space
Mean
Data
Two coins are tossed in an experiment. Which of the following list is the sample space?
S= {HH, HT, TH, TT}
S= {HH, TT}
S= { HT, TH, TT}
S= {HH, HT, TT}
Supposed two coins are tossed consecutively and we are interested in the number of heads that will come out. Determine the values of the random variable H (number of heads).
0,2,3,4
0,1,2,3
0,1,2
0,1,2,3,4
If you had no idea what the answer to this four option multiple choice was and took a wild guess, what is the probability that you are correct?
1/4
1/2
3/4
1
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
209
21
52
43
158
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
72
75
2110
2111
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
1511
124
31
197
218
A fair coin is flipped three times. What is the probability of seeing heads exactly once?
3/8
1/8
1/2
1/6
Find P(X = 2)
5/36
1/12
1/36
1/9
Discrete variable is from qualities that can be
Measured
Counted
Both A and B
none of these
Continuous variable is from qualities that can be
Measured
Counted
Both A and B
none of these
Which of the following is NOT a continuous variable?
A person’s height each year
A person’s weight on each birthday
Number of Cars finished in a factory each day
The volume of water in a swimming pool
Which of these is NOT a discrete variable?
The number of students absent in a class
The number of death per year attributed to lung cancer
The average amount of electricity consumed per household
per month
The number of people who drive through a red light each
hour during rush hour
The number of avocado produced by an avocado tree each year is a continuous variable
True
False
Maybe
Cannot be determined
If two coins are tossed, which is NOT a possible value of the random variable for the number of heads?
0
1
2
3
Which of the following is NOT a true statement?
The value of a random variable could be zero.
Random variables can only have one value.
The probability of all the value of a random variable could be zero.
The sum of all the probabilities in a probability distribution is always equal to one.
You decided to conduct a survey of families with two children. You are interested in counting the number of boys (out of 2 children) in each family. Is this a random variable? If it is, what are the possible values?
Yes, it is a random variable and its value can be 1 or 2.
Yes, it is a random variable and its value can be 0, 1 or 2.
Yes, it is a random variable and its value can be 2 or 4.
No, it is not a random variable since it is not random.
In a local community, a couples were asked the questions “Are you satisfied with the work of the current president?” If the husband and the wife both said “yes”, the response is written as YY. If the husband said yes and the wife said “no”, the response is YN. Let X = the number of “yes” responses. , what are the possible values of the random variables?
0, 1, 2
1, 2, 3
2, 3, 4
1, 1, 2
A quantity resulting from an experiment by chance, can assume a different values is called.
Random Experiment
Random Sample
Random Variable
Random process
What is the sum of the probabilities of all values of the random variable?
∑〖(P(X))〗=0
∑〖(P(X))〗=1/10
∑〖(P(X))〗=1
∑〖(P(X))〗=10
If two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. If the value of the random variable represents the number of blue balls. How many outcomes are possible?
2
4
6
8
Which of the following cannot be the value of probability of the random variable?
1.01
0
1/4
1/2
Which of the following can serve as the values of a probability distribution?
P(1) = 0.42, P2) = 0.31, P(3)= 0.37
P(1) = 9/14, P2) = 4/14, P(3)= 1/14
P(1) = 0.08, P2) = 0.12, P(3)= 1.03
P(1) = 10/33, P2) = 12/33, P(3)= 10/33
If P(X) = X /6 , what are the possible values of X for it to be a probability distribution?
0,2,3
1,2,3
2,3,4
1,1,2
One thousand tickets are sold for ₱10.00 each. One ticket will win ₱2,000.00, two tickets will win ₱1,000.00 each and four tickets will win ₱500.00 each. What is the probability of winning
any amount in the purchase of one ticket?
1/1000
2/1000
5/1000
7/1000
A roulette wheel in a fiesta carnival has the numbers 1 through 50. If you bet ₱5.00, you will have a chance to win a kitchen utensil worth ₱200.00. How much the organizer will earn if 100games will be played?
₱2,000.00
₱3,000.00
₱4,000.00
₱5,000.00
A life insurance company will sell a ₱500,000.00 five-year term life insurance policy exclusive for police enforcers for a premium of ₱1,000.00. Find the expected value to the company of a single policy if a police enforcer has a 99.95% chance of surviving five years?
₱550.00
₱650.00
₱750.00
₱850.00
The total area under the standard normal curve is _________.
-1
0
0.5
1
What is the shape of a Normal Probability Distributions?
bar
bell
circle
line
Which part of a normal curve is extended indefinitely both directions along the horizontal axis, approaching but never touching it?
center
tail
top
spread
Which of the following rule states that almost all data fall within the 1, 2 and 3 of standard deviation of mean when the population is normally distributed?
empirical rule
Pascal’s triangle rule
Lottery rule
Love rule
If the average age of retirement for the population in the Philippines is 65 years and with standard deviation of 5 years, what is the approximate age range in which 68% of people retire?
60 – 70 years
55 – 65 years
55 – 60 years
60 -65 years
What term refers to the body of knowledge that deals with the collection, organization, presentation and analysis of data?
Statistics
Trigonometry
Algebra
Probability
Based on the research conducted by the DOH, “63 % of those found to have diabetes were not aware that they have such disease”. The statement above is an example of _____________.
Inferential Statistics
Individual Statistics
Descriptive Statistics
Differential Statistics
Which is an example of qualitative data?
age of a tree
length of large intestines
color of rainbow
scores in a Mathematics quiz
It is a technique by which data is presented in a paragraph form.
Tabular
Graphical
Textual
One ball is drawn from each of the boxes shown. Find the probability that at most one blue ball is drawn.
2760
6029
6014
2730
If 3 coins are tossed simultaneously, find the probability of getting exactly two tails.
83
32
52
31
John flipped three coins, what is the probability of getting all tails
1/2
1/4
1/8
1/16
If I toss a coin, what is the probability that I will get tails
1/2
1/4
25%
55%
I have 2 dice, how many outcomes are possible if I roll the 2 dice together
12
6
36
24
Suppose P(A)=0.37 , P(B)=0.41 and P(A∪B)=0.78 . Find P(A∩B) .
0.37
0
0.78
0.25
One ball is drawn from each of the boxes shown. Find the probability that at most one blue ball is drawn.
2760
6029
6014
2730
What is the total area under the normal curve in a standard normal distribution?
1
2
3
4
Where can we locate the mean in the normal curve?
to the left portion
to the right portion
at the center
on the z - axis
Which of the following graphs shows a normal curve?
32%
