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Last week, a flower delivery business conducted a survey on customer happiness. They found that $30\%$ of their customers were ＂pleased＂ with the service. $\newline$ If the company surveys $2$ of their customers the next week, what is the probability that $0$ are pleased? $\newline$ 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. Last week, a flower delivery business conducted a survey on customer happiness. They found that

30\%

of their customers were ＂pleased＂ with the service.

\newline

If the company surveys

2

of their customers the next week, what is the probability that

0

are pleased?

\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, $n = 2$ , $k = 0$ , and $p = 0.30$ .
Calculate $C(2, 0)$ : Calculate $C(2, 0)$ which is $\frac{2!}{0! (2 - 0)!}$ . Since $0!$ is $1$ and $2!$ is $2$ , $C(2, 0)$ equals $1$ .
Solve $(0.30)^0$ : Solve $(0.30)^0$ which is $1$ because any number to the power of $0$ is $1$ .
Simplify $(1 - 0.30)^{(2 - 0)}$ : Simplify $(1 - 0.30)^{(2 - 0)}$ which is $(0.70)^2$ .
Calculate $(0.70)^2$ : Calculate $(0.70)^2$ which is $0.70 \times 0.70$ equals $0.49$ .
Multiply Values Together: Multiply all the values together: $1 \times 1 \times 0.49$ equals $0.49$ .
Round to Nearest Thousandth: Round the answer to the nearest thousandth: $0.49$ rounded to the nearest thousandth is $0.490$ .

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