Q15. Guessing the initial of a student's middle name: Identify the sample space and determine the number of outcomes.

Background

Topic: Sample Space in Probability

This question tests your understanding of how to define the sample space for a probability experiment and count the number of possible outcomes.

Key Terms:

• Sample Space: The set of all possible outcomes.

• Outcome: A single possible result of the experiment.

Step-by-Step Guidance

1. Consider what the experiment is: guessing the initial of a student's middle name.

2. Think about the possible initials—typically, these are the 26 letters of the English alphabet.

3. List the sample space: {A, B, C, ..., Z}.

4. Count the number of outcomes in the sample space.

Try solving on your own before revealing the answer!

Q16. Guessing a student's letter grade (A, B, C, D, F) in a class: Identify the sample space and determine the number of outcomes.

Background

Topic: Sample Space in Probability

This question is about identifying the sample space for a categorical variable (letter grades) and counting the outcomes.

Key Terms:

• Sample Space: All possible grades a student could receive.

• Outcome: Each possible grade.

Step-by-Step Guidance

1. Identify the possible grades: A, B, C, D, F.

2. Write the sample space: {A, B, C, D, F}.

3. Count the number of outcomes in the sample space.

Try solving on your own before revealing the answer!

Q17. Drawing one card from a standard deck of cards: Identify the sample space and determine the number of outcomes.

Background

Topic: Sample Space in Probability

This question tests your ability to describe the sample space for a standard deck of cards and count the outcomes.

Key Terms:

• Sample Space: All possible cards in the deck.

• Outcome: Each individual card.

Step-by-Step Guidance

1. Recall that a standard deck has 52 cards, divided into 4 suits (hearts, diamonds, spades, clubs) with 13 cards in each suit.

2. List the sample space: all combinations of rank and suit (e.g., Ace of Hearts, 2 of Diamonds, etc.).

3. Count the number of outcomes in the sample space.

Try solving on your own before revealing the answer!

Q21. A computer is used to randomly select a number from 1 to 2000. Event A is selecting the number 253. Is this a simple event?

Background

Topic: Simple Events in Probability

This question asks you to determine whether an event is simple (consists of a single outcome) or not.

Key Terms:

• Simple Event: An event with only one outcome.

• Outcome: The result of the random selection.

Step-by-Step Guidance

1. Identify the event: selecting the number 253.

2. Determine how many outcomes are in this event (just one: 253).

3. Compare this to the definition of a simple event.

Try solving on your own before revealing the answer!

Q22. A computer is used to randomly select a number from 1 to 4000. Event B is selecting a number less than 500. Is this a simple event?

Background

Topic: Simple Events in Probability

This question tests your ability to distinguish between simple and compound events.

Key Terms:

• Simple Event: An event with only one outcome.

• Compound Event: An event with more than one outcome.

Step-by-Step Guidance

1. Identify the event: selecting a number less than 500.

2. Count the number of outcomes (numbers from 1 to 499).

3. Compare this to the definition of a simple event.

Try solving on your own before revealing the answer!

Q23. You randomly select one card from a standard deck of 52 playing cards. Event A is selecting an ace. Is this a simple event?

Background

Topic: Simple Events in Probability

This question asks you to determine whether selecting an ace from a deck is a simple event.

Key Terms:

• Simple Event: An event with only one outcome.

• Compound Event: An event with more than one outcome.

Step-by-Step Guidance

1. Identify the event: selecting an ace.

2. Count the number of aces in a standard deck (one per suit).

3. Compare this to the definition of a simple event.

Try solving on your own before revealing the answer!

Q24. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ten of diamonds. Is this a simple event?

Background

Topic: Simple Events in Probability

This question tests your understanding of simple events in the context of card selection.

Key Terms:

• Simple Event: An event with only one outcome.

• Outcome: The ten of diamonds.

Step-by-Step Guidance

1. Identify the event: selecting the ten of diamonds.

2. Determine how many outcomes are in this event (just one: ten of diamonds).

3. Compare this to the definition of a simple event.

Try solving on your own before revealing the answer!

Q25. Menu: A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 10 choices for an entree, and 4 choices for a dessert. How many different meals are available when you select an appetizer, an entree, and a dessert?

Background

Topic: Fundamental Counting Principle

This question tests your ability to use the Fundamental Counting Principle to determine the total number of possible combinations.

Key Formula:

Where , , and are the number of choices for each category.

Step-by-Step Guidance

1. Identify the categories: appetizer, entree, dessert.

2. Write the number of choices for each: 5 appetizers, 10 entrees, 4 desserts.

3. Multiply the number of choices for each category to find the total number of possible meals.

Try solving on your own before revealing the answer!

Q26. Laptop: A laptop has 3 choices for a processor, 3 choices for a graphics card, 4 choices for memory, 6 choices for a hard drive, and 2 choices for a battery. How many ways can you customize the laptop?

Background

Topic: Fundamental Counting Principle

This question tests your ability to use the Fundamental Counting Principle for multiple categories.

Key Formula:

Where through are the number of choices for each component.

Step-by-Step Guidance

1. List the categories: processor, graphics card, memory, hard drive, battery.

2. Write the number of choices for each: 3, 3, 4, 6, 2.

3. Multiply the number of choices for each category to find the total number of possible customizations.

Try solving on your own before revealing the answer!

Q27. Reality: A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

Background

Topic: Fundamental Counting Principle with Restrictions

This question tests your ability to apply the Fundamental Counting Principle when there are restrictions on the choices.

Key Formula:

Step-by-Step Guidance

1. Identify the restrictions: first digit (D1) cannot be zero, last digit (D4) must be even.

2. List the possible choices for each digit:

   • D1: 1–9 (9 choices)

   • D2: 0–9 (10 choices)

   • D3: 0–9 (10 choices)

   • D4: 0, 2, 4, 6, 8 (5 choices)

3. Multiply the number of choices for each digit to find the total number of codes.

Try solving on your own before revealing the answer!

Q28. True or False Quiz: Assuming that no questions are left unanswered, in how many ways can a six-question true or false quiz be answered?

Background

Topic: Fundamental Counting Principle

This question tests your ability to use the Fundamental Counting Principle for binary choices.

Key Formula:

Where is the number of questions.

Step-by-Step Guidance

1. Each question has 2 possible answers: true or false.

2. There are 6 questions, so multiply the number of choices for each question.

3. Set up the calculation: or .

Try solving on your own before revealing the answer!