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Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblema 39
Capitolo 9, Problema 39

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.

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Identify the total number of possible outcomes, which is the total number of cards in the deck. Since there are 52 cards, the total number of outcomes is \(52\).
Determine the number of favorable outcomes for the event 'not dealt a king.' Since there are 4 kings in the deck, the number of cards that are not kings is \(52 - 4 = 48\).
Recall that the probability of an event is given by the formula: \(\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).
Substitute the values into the formula: \(\text{Probability(not dealt a king)} = \frac{48}{52}\).
Simplify the fraction if possible to express the probability in simplest form.

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Basic Probability

Probability measures the likelihood of an event occurring, calculated as the ratio of favorable outcomes to total possible outcomes. In this problem, it involves finding the chance of not drawing a king from a deck.
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Introduction to Probability

Counting Outcomes in a Deck of Cards

A standard deck has 52 cards with 4 kings. Understanding the total number of cards and how many are kings is essential to determine favorable and unfavorable outcomes.
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Fundamental Counting Principle

Complement Rule in Probability

The complement rule states that the probability of an event not happening equals one minus the probability that it does happen. Here, finding the probability of not getting a king is easier by subtracting the probability of getting a king from 1.
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Introduction to Probability
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