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Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a7, the seventh term of the sequence. 3, 12, 48, 192, ...
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 9, Problema 19
In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.
Guida verificata passo dopo passo1
Identify the total number of possible outcomes. Since you are dealt one card from a standard deck, the total number of outcomes is 52.
Determine what a picture card is. In a standard deck, picture cards are Jacks, Queens, and Kings.
Count the number of picture cards in the deck. There are 4 suits, and each suit has 3 picture cards (Jack, Queen, King), so multiply 4 by 3 to get the total number of picture cards.
Set up the probability formula: Probability = (Number of favorable outcomes) / (Total number of possible outcomes).
Substitute the values into the formula: Probability = (Number of picture cards) / 52.
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Probability
Probability measures the likelihood of an event occurring, expressed as a ratio of favorable outcomes to total possible outcomes. It ranges from 0 (impossible event) to 1 (certain event). In card problems, probability helps determine how likely it is to draw a specific type of card.
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5:37
Introduction to Probability
Sample Space
The sample space is the set of all possible outcomes in an experiment. For a standard deck of 52 cards, the sample space includes every individual card. Understanding the sample space is essential to calculate probabilities accurately.
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5:37Introduction to Probability
Picture Cards
Picture cards, also called face cards, are the Jack, Queen, and King in each suit. Since there are 4 suits, there are 12 picture cards in total. Identifying the number of favorable outcomes (picture cards) is key to solving the probability question.
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4:23Complementary Events
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