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Home Question Bank Math Probability Archive 2024 November 22

Probability Questions from Nov 22,2024

Browse the Probability Q&A Archive for Nov 22,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the feam members who do nof wear glasses, 30 percent of them are in the 10 th grade. To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade? \( 14 \% \) \( 17 \% \) \( 55 \% \) \( 67 \% \) Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last skater. Then, they try to decide whether or not Oliver should be the first skater in the race. Which subset, \( A \), of the sample space shows the complement of the event in which Oliver is the first skater in the race? \( \begin{array}{l}A=\{M O P N, ~ P M O N ~\end{array} \) \( A=\{O P M N, O M P N\} \) \( A=\{M O P N, M P O N, O P M N, P O M N\} \) \( A=\{M O P N, M P O N, P M O N, P O M N\} \) A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probability that the committee consists of all boys? \( \frac{4}{1001} \) \( \frac{15}{1001} \) \( \frac{10}{143} \) \( \frac{133}{143} \) 2. Se tira un dado. Halla: \begin{tabular}{l|l} a) La probabilidad de que se obtenga un 4 & b) La probabilidad de que se obteng \\ o un 5.\end{tabular} \( \begin{array}{l}\text { número par o un número menor qu }\end{array} \) LYCP1 PMP5: M4 S1- Calculo la probabilidad de eventos compuestos de la forma \( P(A \circ B)=P(A \cup B) \). 1. EN pAREJAs Expliquen con sus propias palabras cuándo dos eventos son compuest cuándo son mutuamente excluyentes y por qué se calcula la probabilidad de estos últi con la fórmula \( P(A \cup B)=P(A)+P(B) \). Obtengan conclusiones; resúmelas por esc en el espacio que sigue. (b) A fair coin is tossed three times. Let the random variable X be the number of heads. (i) State the probability distribution (ii) Compute the expected value and variance of \( X \) (iii) What is the probability of at most two heads (iv) What is the probability of at least two heads (b) A fair coin is tossed three times. Let the random variable X be the number of heads. (i) State the probability distribution (ii) Compute the expected value and variance of \( X \) (iii) What is the probability of at most two heads (iv) What is the probability of at least two heads 1. (a) List the outcomes and the values of X , the sum of the up-turned faces for the experiment of rolling a pair of dice. Construct the probability distribution of the random variable \( X \). Further, calculate \( E(X) \) and \( \operatorname{Var}(X) \). a) Among 44 people at least how many were born in the same month? Answer \( =\square \) Ans people at least how many were born in the same month? (b) Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 4 were born on the same day, not considering the year? Answer \( =\square \)
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