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4. A meteorologist predicts that there is a \( 60 \% \) chance of rain each day for the next three days. You design and perform a simulation that involves randomly generating numbers from 0 to 999 . The digits 1 through 6 represent rain. Which outcome does not represent a favorable outcome? a. exactly one day with rain (the one that has more than one number from \( 1-6 \) ) \( \begin{array}{llll}\text { A. } 968 & \text { B. } 727 & \text { C. } 579 & \text { D. } 111\end{array} \) \( \begin{array}{llll}\text { b. exactly three days with rain (the one with at least one digit that is not } 1-6 \text { ) }\end{array} \) \( \begin{array}{llll}\text { A. } 789 & \text { B. } 456 & \text { C. } 333 & \text { D. } 123\end{array} \) c. rain on the first and last days only (the one that does not have \( 1-6 \) as the first and last digit only) A. 101

Ask by Ray Chavez. in the United States
Mar 14,2025

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The outcomes that do not represent favorable outcomes are **B. 727** and **A. 789**.

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The Deep Dive

If we're looking for an unfavorable outcome in the first choice (exactly one day with rain), let's break down the options! Digits 1 through 6 represent rain, so we need exactly one of those in the three digits generated. The only option that contains more than one digit in that range is B. 727, which has two '7's, thus it doesn’t qualify as “exactly one day.” Now, moving to the second part concerning three days with rain, we still want at least one digit to fall outside the 1-6 range. In this case, option A. 789 is the only one where all digits (7, 8, 9) are outside our rain range. This means it doesn’t satisfy our requirement for three days of rain. Lastly, rain on the first and last days only, and with option A. 101, we've got digit 1 at both ends, which indeed suggests rain on those two days, while the middle digit (0) implies no rain that day - a definite favorable outcome.

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