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Greta and her teammates are each chewing a piece of tropical flavored gum before their championship softball game. 48%48\% of the pieces are pineapple flavored.\newlineIf 33 of her teammates are chosen at random, what is the probability that exactly 11 is chewing pineapple gum?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline

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Q. Greta and her teammates are each chewing a piece of tropical flavored gum before their championship softball game. 48%48\% of the pieces are pineapple flavored.\newlineIf 33 of her teammates are chosen at random, what is the probability that exactly 11 is chewing pineapple gum?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline
  1. Use Binomial Probability Formula: Use the binomial probability formula: P(X=k)=C(n,k)⋅(p)k⋅(1−p)(n−k)P(X = k) = C(n, k) \cdot (p)^k \cdot (1-p)^{(n-k)}. Here, n=3n = 3, k=1k = 1, and p=0.48p = 0.48.
  2. Calculate C(3,1)C(3, 1): Calculate C(3,1)C(3, 1) which is 3!1!×(3−1)!\frac{3!}{1! \times (3 - 1)!}. This simplifies to 31×2\frac{3}{1 \times 2} which equals 32\frac{3}{2}. But wait, that's not right, it should be just 33.

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