Question

let x determine a random variable, and use your knowledge of probability to prepare a probability distribution.
a family has four children and the number of girls is recorded. (assume an equal chance of a boy or girl for each birth.)
complete the probability distribution.

x 0 1 2 3 4
p(x) □ □ □ 1/4 1/16
(type an integer or a simplified fraction.)

Explanation:

#[Client Connection Error] Explanation:

Step1: Calculate the probability for \(x = 0\)

The probability of having a boy (\(p=\frac{1}{2}\)) and a girl (\(q = \frac{1}{2}\)). Using the binomial probability formula \(P(X=k)=C(n,k)\times p^{n - k}\times q^{k}\), where \(n = 4\), \(k = 0\), and \(C(n,k)=\frac{n!}{k!(n - k)!}\).

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Step2: Calculate the probability for \(x = 1\)

For \(n = 4\), \(k = 1\)

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Step3: Calculate the probability for \(x = 2\)

For \(n = 4\), \(k = 2\)

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Answer:

When \(x = 0\), \(P(x)=\frac{1}{16}\); when \(x = 1\), \(P(x)=\frac{1}{4}\); when \(x = 2\), \(P(x)=\frac{3}{8}\)