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Home Question Bank Math Probability Archive 2024 November 23

Probability Questions from Nov 23,2024

Browse the Probability Q&A Archive for Nov 23,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\begin{tabular}{l}\( \left\lvert\, \begin{array}{l}\text { 1. All of the letters in the } \\ \text { alphabet are randomly placed } \\ \text { in a bag. Each letter appears } \\ \text { just once. What is the ratio of } \\ \text { vowels to consonants? } \\ \text { vow }\end{array}\right. \) \\ \hline\end{tabular} 18. En una encuesta se consultó a 120 personas por el tipo de monedas que se encontraban comprando. Ochenta personas estaban comprando dólares, sesenta compraban euros y veinte personas otras monedas que no eran ni dólares ni euros. Si se hubiese escogido una de estas personas al azar, ¿cuál es la probabilidad de que hubiese comprado dólares y euros? 1. A market researcher company has found from experience that three in ten people are willing to participate in focus group interviews. The company has been commissioned to conduct a focus group interview on the consumption patterns of bread for a bakery client. What is the probability that the company will recruit more than three consumers for the interview session if it randomly approached 12 people? A. Airline passengers arrive randomly and independently at the passenger screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. Calculate the probability of at least 3 arrivals in one-minute period. The service time of the first service of a BMW car is found to be normally distributed with a mean of 170 minutes and a standard deviation of 81 minutes. What is the probability that the service plan will take more than 80 minutes? 20. Ramiro y Gonzalo están matriculados en un curso de fotografia. Desde que comenzó el curso, la asistencia a clases de Ramiro ha sido de un \( 80 \% \) y la de Gonzalo de un \( 60 \% \), siendo independientes sus ausencias. Si se ellige un día al azar en que se haya impartido el curso, ¿cuál es la probabilidad de que al menos uno de ellos haya asistido a clases? (b) The number of randomly selected residents, with a probability 0.989 containing at least 10 who have earned at least a bachelor's degree, is nearest integer.) (Round up to the \( p(x\leq 3) \) A binomial probability experinent is conducted with the given parameters, Conpute the probabiity of \( x \) successes in the \( n \) independent trials of the experinent. \( \mathrm{m}=20 . \mathrm{p}=0.7, \mathrm{x}=19 \) \( \mathrm{P}(19)=\square \) (Do not round until the final answer. Then round to four decinal places as needed.) According to flightstats com, American Airlines flights from Dallas to Chicago are on time \( 80 \% \) of the time. Suppose 17 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of \( n \) and \( p \). (c) Find and interpret the probability that exactly 11 flights are on time. (d) Find and interpret the probability that fewer than 11 flights are on time. (e) Find and interpret the probability that at least 11 flights are on time. (f) Find and interpret the probability that between 9 and 11 flights, inclusive, are on time. A. Each trial depends on the previous trial. (a) Identify the statements that explain why this is a binomial experiment. Select all that apply. \( \square \) B. The experiment is performed a fixed number of times. \( \square \) C. The probability of success is the same for each trial of the experiment. \( \square \) D. The trials are independent. \( \square \) E. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late. \( \square \) F. The experiment is performed until a desired number of successes are reached. \( \square \) G. The probability of success is different for each trial of the experiment. \( \square \) H. There are two mutually exclusive outcomes, success or failure. A binomial probability experiment is conducted with the given parameters. Compute the probability of \( x \) successes in the \( n \) independent trials of the experiment. \( n=9, p=0.2, x \leq 3 \) The probability of \( x \leq 3 \) successes is \( \square \). (Round to four decimal places as needed.) A binomial probability experiment is conducted with the given parameters. Compute the probability of \( x \) successes in the \( n \) independent trials of the experiment. \( n=12, p=0.35, x=2 \) \( P(2)=\square \) (Do not round untit the final answer. Then round to four decimal places as needed.)
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