BIG IDEAS MATH H2O i REASONING Each letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z? Write your answer as a fraction or percent rounded to the nearest tenth. The theoretical probability of choosing a letter other than Z is Previous

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Let $$ n $$ be the total number of letters in the alphabet, so $$ n = 26 $$.

There is 1 letter $$ Z $$ that we need to exclude, so the number of letters that are not $$ Z $$ is $$ 26 - 1 = 25 $$.

The theoretical probability $$ P $$ of choosing a letter other than $$ Z $$ is given by:
$$
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{25}{26}
$$

To express this probability as a percent, we calculate:
$$
\frac{25}{26} \times 100 \approx 96.2\%
$$

Thus, the theoretical probability of randomly choosing any letter except $$ Z $$ is 
$$
\frac{25}{26} \quad \text{or approximately } 96.2\%.
$$
The probability of choosing any letter except Z is $$ \frac{25}{26} $$ or approximately 96.2%.

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