Textbook Question
Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58. If {an} is a finite sequence whose last term is -83, how many terms does {an} contain?
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 53
If you toss a fair coin six times, what is the probability of getting all heads?
Verified step by step guidance1
Understand that each coin toss is an independent event with two possible outcomes: heads or tails, each with a probability of \(\frac{1}{2}\).
Since the coin is fair, the probability of getting heads on a single toss is \(\frac{1}{2}\).
To find the probability of getting all heads in six tosses, multiply the probability of heads for each toss together because the events are independent.
Express this multiplication as \(\left(\frac{1}{2}\right)^6\), which represents the probability of heads on toss 1 AND toss 2 AND ... AND toss 6.
This expression gives the probability of getting all heads in six tosses without calculating the final numerical value.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability of a Single Event
Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. For a fair coin, the probability of getting heads in one toss is 1/2, since there are two equally likely outcomes.
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Probability of Mutually Exclusive Events
Independent Events
Events are independent if the outcome of one does not affect the others. Tossing a coin multiple times are independent events, so the probability of multiple outcomes is the product of their individual probabilities.
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5:54Probability of Multiple Independent Events
Multiplication Rule for Independent Events
To find the probability of several independent events all occurring, multiply their individual probabilities. For six coin tosses all resulting in heads, multiply (1/2) six times, resulting in (1/2)^6.
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Related Practice
Textbook Question
Use the formula for nCr to solve Exercises 49–56. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?
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Textbook Question
In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)
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Textbook Question
Use the graphs of the arithmetic sequences {a} and {b} to solve Exercises 51-58.
Find a14+b12.
Textbook Question
In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an = 2n
Textbook Question
Find f(x + h) − f(x)/h and simplify. f(x) = x4+7