It is believed that 71% of tickets purchased for an upcoming music festival are actually legitimate tickets. The rest are fake tickets sold by scam artists. Assume everyone who bought a ticket shows up at the concert. If security guards at the festival randomly select 4 tickets to examine in more detail, what is the probability that exactly 1 of those tickets is legitimate? Write your answer as a decimal rounded to the nearest thousandth. ____

Use Binomial Probability Formula: Use the binomial probability formula: P(X = k) = C(n, k) * (p)^k * (1-p)^(n-k). Here, n = 4, k = 1, and p = 0.71.Calculate C(4, 1): Calculate C(4, 1) which is 4! / (1! * (4 - 1)!). That's 4 / 1 which is 4.Calculate (0.71)^1: Now calculate (0.71)^1 which is just 0.71.Calculate (1 - 0.71)^(4 - 1): Next, calculate (1 - 0.71)^(4 - 1). That's (0.29)^3.Calculate (0.29)^3: (0.29)^3 equals 0.29 * 0.29 * 0.29, which is 0.024389.Multiply All Values Together: Now multiply all the values together: 4 * 0.71 * 0.024389.The multiplication gives us 4 * 0.71 * 0.024389 equals 0.0692 when rounded to the nearest thousandth.

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It is believed that $71\%$ of tickets purchased for an upcoming music festival are actually legitimate tickets. The rest are fake tickets sold by scam artists. Assume everyone who bought a ticket shows up at the concert. $\newline$ If security guards at the festival randomly select $4$ tickets to examine in more detail, what is the probability that exactly $1$ of those tickets is legitimate? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

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Math Problems

Algebra 2

Find probabilities using the binomial distribution

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Q. It is believed that

71\%

of tickets purchased for an upcoming music festival are actually legitimate tickets. The rest are fake tickets sold by scam artists. Assume everyone who bought a ticket shows up at the concert.

\newline

If security guards at the festival randomly select

4

tickets to examine in more detail, what is the probability that exactly

1

of those tickets is legitimate?

\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, $n = 4$ , $k = 1$ , and $p = 0.71$ .
Calculate $C(4, 1)$ : Calculate $C(4, 1)$ which is $\frac{4!}{1! \times (4 - 1)!}$ . That's $\frac{4}{1}$ which is $4$ .
Calculate $(0.71)^1$ : Now calculate $(0.71)^1$ which is just $0.71$ .
Calculate $(1 - 0.71)^{(4 - 1)}$ : Next, calculate $(1 - 0.71)^{(4 - 1)}$ . That's $(0.29)^3$ .
Calculate $(0.29)^3$ : $(0.29)^3$ equals $0.29 \times 0.29 \times 0.29$ , which is $0.024389$ .
Multiply All Values Together: Now multiply all the values together: $4 \times 0.71 \times 0.024389$ .
Multiply All Values Together: Now multiply all the values together: $4 \times 0.71 \times 0.024389$ .The multiplication gives us $4 \times 0.71 \times 0.024389$ equals $0.0692$ when rounded to the nearest thousandth.