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Chapter 21: Exploring Concepts of Probability
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) Assessing young students on probability knowledge, what would the expectation be that they
would be able to do?
A) Explain their confidence in a theory result.
B) Determine the probability of an experiment.
C) Tell whether an event is likely or not.
D) Write reports about the probability of a real situation.
2) Tools that could be used by young students to model probability experiments include all of the
following EXCEPT:
A) Spinners (virtual and manual).
B) Weather forecasts.
C) Coin tosses.
D) Marbles pulled out of bag.
3) Identify the term that is used to for the measure of the probability of an event occurring.
A) Experimental probability.
B) Theoretical probability.
C) Relative frequency.
D) An observed occurrence.
4) This phenomenon refers to a probability experiment being carried out more and more times so
that the recorded results get close to theoretical probability.
A) The law of averages.
B) The law of likelihood.
C) The law of large numbers.
D) A law of small numbers.
5) The process for teaching probability can and should be taught through a problem-based
approach. What phase of this process would occur in the “after” portion of the lesson?
A) Concrete exploration.
B) Representation.
C) Construction.
D) Present symbolically and diagrammatically.
6) Conducting experiments and examining outcomes in teaching is important. All of these help
address student misconceptions EXCEPT:
A) Provide a connection to counting strategies.
B) Helps students learn more than students who do not engage in doing experiments.
C) Model real-world problems.
D) It is significantly more intuitive and fun.
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7) All of the following can be used to model and record the results of two independent events
EXCEPT:
A) Tree diagram.
B) Table.
C) Pair of dice.
D) Stem and leaf plot.
8) Identify the description of an experiment of dependent events.
A) The probability of drawing a certain marble out of a bag on two different tries, replacing the
first marble before drawing out a second.
B) Drawing two cards from a deck, if, when you draw the first, you leave it out, then draw the
second.
C) The probability of getting an even number after rolling a die, then rolling it again.
D) The probability of obtaining heads after flipping a coin once, then a second time.
9) What is the mathematical term that describes probability as the comparison of desired
outcomes to the total possible outcomes?
A) Fraction.
B) Ratio.
C) Relative frequency.
D) Experimental probability.
10) Students can often determine the number of outcomes on some random devices than others.
Identify the random device that is challenging and students need more experience.
A) Coin toss.
B) 8- sided die.
C) Spinners.
D) Two color counters.
11) Probability has two distinct types. Identify the event below that the probability would be
known.
A) What is the possibility of Luke H. making all his free throws?
B) What is the chance of a snowstorm in Minnesota in January?
C) What is the probability of rolling a 4 with a fair die?
D) What is the probability of dropping a rock in water and it will sink?
12) A number line with 0 (impossible) to 1(possible) is purposeful when students are learning
about probability. All of the statements would be examples of benefits of a number line
EXCEPT:
A) Provides a visual representation.
B) Connects to the likelihood of an event occurring.
C) Reference for talking about probability.
D) Experimental random device.
13) Truly random events occur in unexpected groups, a fair coin may turn up heads five times in
a row; a 100-year flood may hit a town twice in 10 years. This imperfect probability is called
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A) Distribution of randomness.
B) Probability inequality.
C) Sampling size error.
D) Measure of chance.
14) The following experiments are examples of probabilities with independent events EXCEPT:
A) Rolling two dice and getting a difference that is not more than 3.
B) Having a tack or cup land up when each is tossed once.
C) Drawing a certain marble out of a bag on two different tries, replacing the first marble before
drawing out a second.
D) Spinning blue twice on a spinner.
15) The process for helping students connect sample space to probability includes all of the steps
EXCEPT:
A) Conduct an experiment with a large number of trials.
B) Create a comparison experiment.
C) Predict the results of the experiment.
D) Compare the prediction with the experiment.
16) What type of probability recording method is less abstract and accessible to a larger range of
learners?
A) Tree diagram.
B) Dot plot.
C) Area representation.
D) Equation.
17) What is the probability misconception called when students think that an event that has
already happened will influence the outcome of the next event?
A) Law of small numbers.
B) Possibility counting.
C) Commutativity confusion.
D) Gambler’s fallacy.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
18) Describe two activities that can help develop probability concepts for students.
19) How do experiments support student learning about probability?
