Tammy hosts a trivia night at her house every Thursday. She generates questions using a trivia website. The website claims that there is a 29% chance that a generated question is a history question. If the claim is correct, and Tammy randomly generates 5 questions during the first round of trivia, what is the probability that exactly 1 will be a history question? 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 = 5, k = 1, and p = 0.29.Calculate C(5, 1): Calculate C(5, 1) which is the number of ways to choose 1 question out of 5. C(5, 1) = 5! / (1! * (5 - 1)!) = 5.Calculate (0.29)^1: Calculate (0.29)^1 which is the probability of getting exactly 1 history question. (0.29)^1 = 0.29.Calculate (1 - 0.29)^(5 - 1): Calculate (1 - 0.29)^(5 - 1) which is the probability of not getting a history question in the other 4 questions. (1 - 0.29)^(5 - 1) = (0.71)^4.Calculate (0.71)^4: (0.71)^4 = 0.71 * 0.71 * 0.71 * 0.71 = 0.25411681.Calculate Probability P(X = 1): P(X = 1) = 5 * 0.29 * 0.25411681. Multiply all the values together to find the probability.Final Calculation: P(X = 1) = 5 * 0.29 * 0.25411681 = 0.368369165. Round this to the nearest thousandth.Rounded Answer: Rounded answer: 0.368.

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Tammy hosts a trivia night at her house every Thursday. She generates questions using a trivia website. The website claims that there is a $29\%$ chance that a generated question is a history question. $\newline$ If the claim is correct, and Tammy randomly generates $5$ questions during the first round of trivia, what is the probability that exactly $1$ will be a history question? $\newline$ Write your answer as a decimal rounded to the nearest thousandth. $\newline$ ____ $\newline$

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Algebra 2

Find probabilities using the binomial distribution

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Q. Tammy hosts a trivia night at her house every Thursday. She generates questions using a trivia website. The website claims that there is a

29\%

chance that a generated question is a history question.

\newline

If the claim is correct, and Tammy randomly generates

5

questions during the first round of trivia, what is the probability that exactly

1

will be a history question?

\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, $n = 5$ , $k = 1$ , and $p = 0.29$ .
Calculate $C(5, 1)$ : Calculate $C(5, 1)$ which is the number of ways to choose $1$ question out of $5$ . $C(5, 1) = \frac{5!}{1! * (5 - 1)!} = 5$ .
Calculate $(0.29)^1$ : Calculate $(0.29)^1$ which is the probability of getting exactly $1$ history question. $(0.29)^1 = 0.29$ .
Calculate $(1 - 0.29)^{(5 - 1)}$ : Calculate $(1 - 0.29)^{(5 - 1)}$ which is the probability of not getting a history question in the other $4$ questions. $(1 - 0.29)^{(5 - 1)} = (0.71)^4$ .
Calculate $(0.71)^4$ : $(0.71)^4 = 0.71 \times 0.71 \times 0.71 \times 0.71 = 0.25411681$ .
Calculate Probability $P(X = 1)$ : $P(X = 1) = 5 \times 0.29 \times 0.25411681$ . Multiply all the values together to find the probability.
Final Calculation: $P(X = 1) = 5 \times 0.29 \times 0.25411681 = 0.368369165$ . Round this to the nearest thousandth.
Rounded Answer: Rounded answer: $0.368$ .