Questions: Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. Drawing three kings in a row from a standard deck of cards when the drawn card is returned to the deck each time Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) A. The individual events are dependent. The probability of the combined event is . B. The individual events are independent. The probability of the combined event is

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
Drawing three kings in a row from a standard deck of cards when the drawn card is returned to the deck each time

Select the correct choice below and fill in the answer box to complete your choice.
(Simplify your answer.)
A. The individual events are dependent. The probability of the combined event is .
B. The individual events are independent. The probability of the combined event is

Transcript text: Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. Drawing three kings in a row from a standard deck of cards when the drawn card is returned to the deck each time Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) A. The individual events are dependent. The probability of the combined event is $\square$ . B. The individual events are independent. The probability of the combined event is $\square$

Solution

Paso 1: Determinación de la independencia de los eventos

Al devolver la carta al mazo después de cada extracción, la probabilidad de sacar un rey se mantiene constante en cada intento. Por lo tanto, los eventos son independientes.

Paso 2: Cálculo de la probabilidad de sacar un rey

La probabilidad de sacar un rey en un solo intento es:

\[ P(K) = \frac{4}{52} = \frac{1}{13} \approx 0.0769 \]

Paso 3: Cálculo de la probabilidad del evento combinado

Dado que los eventos son independientes, la probabilidad de sacar tres reyes en fila es:

\[ P(K \text{ en 3 intentos}) = P(K) \times P(K) \times P(K) = \left(\frac{1}{13}\right)^3 = \frac{1}{2197} \approx 0.0004552 \]

Respuesta Final

La respuesta correcta es B. Los eventos individuales son independientes. La probabilidad del evento combinado es \$\boxed{\frac{1}{2197}}\$.

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