Questions: A trail mix contains a mixture of nuts: pecans, walnuts, hazelnuts, and peanuts. If the probability of reaching into the trail mix and getting pecans is 0.09, what is the probability of not getting pecans? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest hundredth.

A trail mix contains a mixture of nuts: pecans, walnuts, hazelnuts, and peanuts. If the probability of reaching into the trail mix and getting pecans is 0.09, what is the probability of not getting pecans? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest hundredth.
Transcript text: A trail mix contains a mixture of nuts: pecans, walnuts, hazelnuts, and peanuts. If the probability of reaching into the trail mix and getting pecans is 0.09, what is the probability of not getting pecans? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest hundredth.
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Solution

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Solution Steps

Step 1: Identify the Probability P(A)

The probability of selecting item A, denoted as \(P(A)\), is given as 0.09.

Step 2: Calculate the Probability of Not Selecting the Item \(P(\neg A)\)

To find \(P(\neg A)\), we subtract \(P(A)\) from 1: \(P(\neg A) = 1 - P(A)\). Substituting the given value of \(P(A) = 0.09\), we get \(P(\neg A) = 0.91\).

Step 3: Express \(P(\neg A)\) in the Required Format

After rounding to 2 decimal places, \(P(\neg A)\) is approximately 0.91.

Final Answer:

The probability of not selecting item A, \(P(\neg A)\), rounded to 2 decimal places, is 0.91.

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