Twenty-six slips of paper are each marked with a different...

Twenty-six slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled out, its letter recorded (in the order in which the slip was drawn), and the slip is replaced. This is done 5 times. Find the probabilities that the following "words" are formed. A word that contains no $" x, " y, "$ or $^{4} z^{\prime \prime}$

Twenty-six slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled out, its letter recorded (in the order in which the slip was drawn), and the slip is replaced. This is done 5 times. Find the probabilities that the following "words" are formed.
A word that contains no $" x, " y, "$ or $^{4} z^{\prime \prime}$

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Key Concepts

Counting Principles

Counting principles, like the multiplication principle, are used to determine the total number of outcomes by multiplying the number of choices at each stage. This approach is essential when calculating probabilities in multi-step experiments.

Sample Space

The sample space of an experiment is the set of all possible outcomes. For example, drawing a letter from 26 possibilities over 5 independent draws creates a sample space of 26^5 outcomes.

Probability Calculation

Probability calculation involves finding the ratio of favorable outcomes to the total outcomes in the sample space. Here, probabilities are computed by determining the number of outcomes that satisfy certain conditions and then dividing by the total number of possible outcomes.

Replacement

In probability, replacement refers to returning the selected item back to the set, ensuring that each draw has the same probability distribution. This concept is crucial for maintaining independence between the draws.

Independent Events

Independent events are those where the outcome of one event does not affect the outcomes of another. With replacement, each draw is independent, meaning the probability remains constant across all draws.

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