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Home Question Bank Math Probability Archive 2024 November 01

Probability Questions from Nov 01,2024

Browse the Probability Q&A Archive for Nov 01,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. If two events are independent, \( P(A \mid B)=P(B) \). Choose the correct answer below. A. True B. False; if events \( A \) and \( B \) are independent, then \( P(B \mid A)=P(A) \). C. False; if events \( A \) and \( B \) are independent, then \( P(A \) and \( B)=P(A) \cdot P(B) \). D. False; if events \( A \) and \( B \) are independent, then \( P(A \) and \( B)=0 \). Explain how the complement can be used to find the probability of getting at least one item of a particular type. Choose the correct answer below. A. The complement of "at least one" is "all." So, the probability of getting at least one item is equal to P(all items) - 1 . B. The complement of "at least one" is "none. "So, the probability of getting at least one item is equal to P(none of the items) -1 . C. The complement of "at least one" is "none." So, the probability of getting at least one item is equal to \( 1-\mathrm{P} \) (none of the items). D. The complement of "at least one" is "all." So, the probability of getting at least one item is equal to \( 1-\mathrm{P} \) (all items). Si un experimento tiene 4 resultados posibles y se repite 3 veces, ¿cuántos resultados posibles hay en total? Al lanzar Un dado dos Veces determinar las posibili. dades de a) Que la Suma \( \xrightarrow{\text { mayra }} 9 \) b) Suma \( >10 \) c) suma \( <5 \) (a) List an example of two events that are independent. (b) List an example of two events that are dependent. (a) List an example of two events that are independent. Choose the correct answer below. A. A father having hazel eyes and a daughter having hazel eyes B. Rolling a die twice C. Not putting money in a parking meter and getting a parking ticket D. Selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck TRY IT 3.19 A student goes to the library. Let events \( B= \) the student checks out a book and \( D= \) the student checks out a DVD. Suppose that \( P(B)=0.40, P(D)=0.30 \) and \( P(D \mid B)=0.5 \). a. Find \( P(B) \). b. Find \( P(D \) AND \( B) \). c. Find \( P(B \mid D) \). d. Find \( P(D \) AND \( B) \). e. Find \( P(D \mid B) \). (2.) Observa la siguiente demostración y explica cada uno de los pasos. Dados dos sucesos, \( A \) y \( B \), el suceso \( A \) se puede ex- presar como la unión de dos sucesos incompatibles: \[ A=(A \cap B) \cup(A-B) \] \( P(A)=P(A \cap B)+P(A-B) \), y, por lo tanto, \( P(A-B)=P(A)-P(A \cap B) \) 1. Supongamos que en promedio se producen 4 accidentes de tráfico al día en una intersección. A) Calcular la probabilidad de que ocurran exactamente 2 accidentes en un día determinado. B) Calcular la probabilidad de que ocurran un máximo de 5 accidentes en un día. C) Calcular la probabilidad de que ocurran 6 accidentes en 2 días consecutivos. C. Evaluate the following combinations a. \( { }_{8} C_{5} \) b. \( { }_{15} C_{3} \) c. \( \binom{10}{1} \) 3 Se lanza dos veces un dado cúbico, con sus caras numeradas del 1 al 6 . Calcula: a. La probabilidad de obtener 6 . b. La probabilidad de no obtener 6 . c. Si participaras en esce juego, iqué podrlas prede. cir de los resultados?
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