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Greta and her teammates are each chewing a piece of tropical flavored gum before their championship softball game. $48\%$ of the pieces are pineapple flavored. $\newline$ If $3$ of her teammates are chosen at random, what is the probability that exactly $1$ is chewing pineapple gum? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

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Find probabilities using the binomial distribution

Full solution

Q. Greta and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.

48\%

of the pieces are pineapple flavored.

\newline

If

3

of her teammates are chosen at random, what is the probability that exactly

1

is chewing pineapple gum?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

____

\newline

Use Binomial Probability Formula: Use the binomial probability formula: $P(X = k) = C(n, k) \cdot (p)^k \cdot (1-p)^{(n-k)}$ . Here, $n = 3$ , $k = 1$ , and $p = 0.48$ .
Calculate $C(3, 1)$ : Calculate $C(3, 1)$ which is $\frac{3!}{1! \times (3 - 1)!}$ . This simplifies to $\frac{3}{1 \times 2}$ which equals $\frac{3}{2}$ . But wait, that's not right, it should be just $3$ .

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