Pregunta
Suppose that events \( E \) and \( F \) are independent. In addition, possible \( P(E)=0.45 \) and \( P(F)=0.2 \). What is \( P(E \) and \( F) \) ? \( P(E \) and \( F)=\square \) (Simplify your answer. Do not round.)
Ask by Peters Ortiz. in the United States
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( P(E \text{ and } F) = 0.09 \)
Solución
To find \( P(E \text{ and } F) \) for independent events, we use the formula:
\[
P(E \text{ and } F) = P(E) \times P(F)
\]
Given that \( P(E) = 0.45 \) and \( P(F) = 0.2 \), we have:
\[
P(E \text{ and } F) = 0.45 \times 0.2 = 0.09
\]
Thus, the answer is:
\[
P(E \text{ and } F) = 0.09
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
When two events \( E \) and \( F \) are independent, the probability of both events occurring, denoted \( P(E \text{ and } F) \), is given by the product of their individual probabilities. Thus, you can use the formula: \[ P(E \text{ and } F) = P(E) \times P(F) \] Plugging in the given values: \[ P(E \text{ and } F) = 0.45 \times 0.2 = 0.09 \] So, \[ P(E \text{ and } F) = 0.09 \]

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