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Danielle and her teammates are each chewing a piece of tropical flavored gum before their championship softball game. 86%86\% of the pieces are pineapple flavored.\newlineIf 33 of her teammates are chosen at random, what is the probability that 00 are chewing pineapple gum?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline

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Q. Danielle and her teammates are each chewing a piece of tropical flavored gum before their championship softball game. 86%86\% of the pieces are pineapple flavored.\newlineIf 33 of her teammates are chosen at random, what is the probability that 00 are chewing pineapple gum?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline
  1. Find Probability of Not Pineapple: First, we need to find the probability of one person not chewing pineapple gum. Since 86%86\% are pineapple, 100%−86%=14%100\% - 86\% = 14\% are not pineapple.
  2. Convert Percentage to Decimal: Now, convert the percentage to a decimal for calculations. 14%14\% as a decimal is 0.140.14.
  3. Calculate Probability of All Not Pineapple: Next, calculate the probability that all three chosen teammates are not chewing pineapple gum. Multiply the probability for one person not chewing pineapple gum three times: 0.14×0.14×0.140.14 \times 0.14 \times 0.14.
  4. Perform Multiplication: Perform the multiplication: 0.14×0.14×0.14=0.0027440.14 \times 0.14 \times 0.14 = 0.002744.
  5. Round to Nearest Thousandth: Finally, round the result to the nearest thousandth: 0.0027440.002744 rounds to 0.0030.003.

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