Exam 19: Investigating Probability

Teacher Licensing Examination Questions Praxis: A two-sided coin is unfairly weighted so that when it is tossed, the probability that heads will result is twice the probability that tails will result. If the coin is to be tossed three separate times, what is the probability that tails will result on exactly two of the tosses?

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Question 1

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A student took the letters M, A, T and wrote down the possibilities MAT, MTA, TAM, TMA, ATM, AMT from the given three letters. When the student wrote out the 6 possibilities, he was finding the

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Question 2

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Explain the connection between tossing coins and Pascal's Triangle.

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Tossing coins and Pascal's Triangle are connected through the concept of probability. When you toss a coin, there are two possible outcomes - heads or tails. This can be represented as a binomial distribution, where the coefficients of the expansion of (a+b)^n form Pascal's Triangle.

Pascal's Triangle is a triangular array of numbers in which each number is the sum of the two directly above it. This triangle can be used to calculate the coefficients of the expansion of binomial expressions, such as (a+b)^n.

When you toss a coin multiple times, you can use Pascal's Triangle to calculate the probability of getting a certain number of heads or tails. For example, if you toss a coin 3 times, you can use Pascal's Triangle to find the probabilities of getting 0, 1, 2, or 3 heads.

In this way, tossing coins and Pascal's Triangle are connected through the application of probability and the calculation of binomial coefficients.

The probability of an event can be determined by:

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Question 4

TIMSS: In a school there were 1,200 students (boys and girls). A sample of 100 students was selected at random, and 45 boys were found in the sample. Which of these is most likely to be the number of boys in the school?

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Question 5

What is the probability that a day in the month of March has a 2 in it?

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Question 6

For all probabilities ( p ), which option is correct?

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Question 7

In a school with 2,400 students, a random sample of 100 students included 45 boys. Based on this sample, how many boys attend the school?

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Question 8

A bag has 6 green marbles and 3 blue marbles. You pick out a blue marble. If you do not put the marble back, what is the probability of now selecting a green marble?

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Question 9

Children who are susceptible to the gambler's fallacy believe that:

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Question 10

Design an expected value experiment using geometric probability. Explain how your experiment yields the expected value.

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Question 11

Explain the differences between historical and mathematical probability.

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Question 12

Sundaes at an ice cream shop have either vanilla or chocolate ice cream; marshmallow, strawberries, or hot fudge for toppings; and either a cherry or peanuts as a garnish. How many sundae combinations are possible?

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Question 13

NAEP: There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected?

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Question 14

A 40% chance of snow means the probability of snow is:

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Question 15

Display the face of a spinner that has the following theoretical probabilities: 1 - 25% 2 - 50% 3 - 12.5% 4 - 12.5%

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Question 16

PISA: A documentary was broadcast about earthquakes and how often they occur. It included a discussion about the predictability of earthquakes. A geologist stated: "In the next twenty years, the chance that an earthquake will occur in Zed City is two out of three." Which of the following best reflects the meaning of the geologist's statement ?

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Question 17

A fair spinner with four colors on its face must have the following be true except:

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Question 18

Design a target that has the following probabilities for hitting various shapes: Square 20% Rectangle 10% Triangle 25% Background 45%

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Question 19

Probability plays a role in each of the following games except:

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Question 20

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A student took the letters M, A, T and wrote down the possibilities MAT, MTA, TAM, TMA, ATM, AMT from the given three letters. When the student wrote out the 6 possibilities, he was finding the

Explain the connection between tossing coins and Pascal's Triangle.

The probability of an event can be determined by:

TIMSS: In a school there were 1,200 students (boys and girls). A sample of 100 students was selected at random, and 45 boys were found in the sample. Which of these is most likely to be the number of boys in the school?

What is the probability that a day in the month of March has a 2 in it?

For all probabilities ( p ), which option is correct?

In a school with 2,400 students, a random sample of 100 students included 45 boys. Based on this sample, how many boys attend the school?

A bag has 6 green marbles and 3 blue marbles. You pick out a blue marble. If you do not put the marble back, what is the probability of now selecting a green marble?

Children who are susceptible to the gambler's fallacy believe that:

Design an expected value experiment using geometric probability. Explain how your experiment yields the expected value.

Explain the differences between historical and mathematical probability.

Sundaes at an ice cream shop have either vanilla or chocolate ice cream; marshmallow, strawberries, or hot fudge for toppings; and either a cherry or peanuts as a garnish. How many sundae combinations are possible?

NAEP: There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected?

A 40% chance of snow means the probability of snow is:

Display the face of a spinner that has the following theoretical probabilities: 1 - 25% 2 - 50% 3 - 12.5% 4 - 12.5%

A fair spinner with four colors on its face must have the following be true except:

Design a target that has the following probabilities for hitting various shapes: Square 20% Rectangle 10% Triangle 25% Background 45%

Probability plays a role in each of the following games except:

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Problem-Solving Strategies

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Extending Computational Fluency With Larger Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

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