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Let the sample space be \( S=\{1,2,3,4,5,6,7,8,9,10\} \). Suppose the outcomes are equally likely. Compute the probability of the event \( E= \) "an even number." \( P(E)=\square \) (Type an integer or a decimal. Do not round.)

Ask by Newton John. in the United States
Mar 19,2025

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The probability of event \( E \) is 0.5.

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Bonus Knowledge

To determine the probability of event \( E \), we first identify the even numbers in the sample space \( S=\{1,2,3,4,5,6,7,8,9,10\} \). The even numbers in this set are \( \{2, 4, 6, 8, 10\} \). There are 5 even numbers. The total number of outcomes in \( S \) is 10. The probability of event \( E \) is calculated by dividing the number of favorable outcomes (even numbers) by the total number of outcomes. So, the probability \( P(E) \) is: \[ P(E) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{5}{10} = 0.5 \] Thus, \[ P(E) = 0.5 \]

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