Pregunta
(d) \( n=1, p=0.27, X=0 \) \( P(X)=\square \)
Ask by Medina Adkins. in the United States
Mar 22,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( P(X=0) = 0.73 \)
Solución
We start with the binomial probability formula:
\[
P(X=k)=\binom{n}{k} p^k (1-p)^{n-k}
\]
For \( n=1 \), \( p=0.27 \), and \( k=0 \):
1. Calculate the binomial coefficient:
\[
\binom{1}{0}=1
\]
2. Compute \( p^0 \):
\[
(0.27)^0=1
\]
3. Compute \( (1-p)^{1-0} \):
\[
(1-0.27)^{1}=0.73
\]
Multiply the results together:
\[
P(X=0)=1 \times 1 \times 0.73=0.73
\]
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Simplifique esta solución Bonus Knowledge
To calculate \( P(X=0) \), where \( n=1 \) and \( p=0.27 \), we can use the formula for the probability of a specific outcome in a binomial distribution. The formula is given by: \[ P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} \] For \( k=0 \), the equation simplifies to: \[ P(X=0) = \binom{1}{0} (0.27)^0 (1-0.27)^{1-0} = 1 \cdot 1 \cdot (0.73) = 0.73 \] So, \( P(X=0) = 0.73 \). Now go celebrate with some imaginary confetti for successfully solving that probability! 🎉
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