unit 12 probability homework 1 answer key

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03-02-2025

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Unit 12 Probability Homework 1: Answer Key & Comprehensive Guide

This guide provides answers and detailed explanations for a hypothetical Unit 12 Probability Homework 1. Since I don't have access to your specific homework assignment, I'll create example problems covering common probability concepts found in introductory probability units. You can adapt these examples and explanations to fit your actual problems. Remember to always refer to your textbook and class notes for specific formulas and terminology used by your instructor.

Understanding Probability Fundamentals:

Before diving into the answer key, let's refresh some key concepts:

• Probability: The likelihood of an event occurring. It's expressed as a number between 0 and 1 (or 0% and 100%). 0 means the event is impossible, and 1 means it's certain.

• Experiment: A process that leads to an outcome. (e.g., flipping a coin, rolling a die).

• Outcome: A possible result of an experiment. (e.g., heads, tails; rolling a 3).

• Sample Space: The set of all possible outcomes.

• Event: A subset of the sample space; a specific outcome or collection of outcomes. (e.g., getting an even number when rolling a die).

Example Problems & Solutions:

Let's assume your homework covered these topics. Replace these with your actual problems.

Problem 1: Simple Probability

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a red marble?

Answer:

• Total marbles: 5 + 3 + 2 = 10
• Number of red marbles: 5
• Probability of drawing a red marble: 5/10 = 1/2 or 50%

Problem 2: Probability with Multiple Events

A fair coin is flipped twice. What is the probability of getting at least one head?

Answer:

• Sample space: {HH, HT, TH, TT} (where H = heads, T = tails)
• Favorable outcomes (at least one head): {HH, HT, TH}
• Probability: 3/4 or 75%

Problem 3: Conditional Probability

A box contains 4 red balls and 6 blue balls. You draw one ball, and without replacing it, you draw a second ball. What is the probability that both balls are red?

Answer:

• Probability of drawing a red ball first: 4/10
• Probability of drawing a second red ball (given the first was red): 3/9 (since one red ball has already been removed)
• Probability of both events happening: (4/10) * (3/9) = 12/90 = 2/15

Problem 4: Independent Events

You roll a die and flip a coin. What is the probability of rolling a 6 and getting heads?

Answer:

Since these are independent events, we can multiply their individual probabilities:

• Probability of rolling a 6: 1/6
• Probability of getting heads: 1/2
• Probability of both events: (1/6) * (1/2) = 1/12

Problem 5: Mutually Exclusive Events

A card is drawn from a standard deck of 52 cards. What is the probability of drawing either a king or a queen?

Answer:

• Probability of drawing a king: 4/52
• Probability of drawing a queen: 4/52
• Probability of drawing a king OR a queen (since these are mutually exclusive): 4/52 + 4/52 = 8/52 = 2/13

Further Help and Resources:

Remember to consult your textbook, class notes, and your instructor for further assistance. Online resources like Khan Academy and other educational websites offer excellent tutorials and practice problems on probability. Understanding the fundamental concepts is crucial to solving more complex probability problems. Good luck with your studies!