Question

in a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. if a household is selected at random, what is the expected number of children in that household? hint: a probability table may be helpful.

Explanation:

Step1: Calculate the expected value formula

The formula for the expected value \(E(X)\) is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) is the value and \(p_i\) is the corresponding probability.

Step2: Substitute the values into the formula

Here, \(x_1 = 1\), \(p_1=0.3\); \(x_2 = 2\), \(p_2 = 0.43\); \(x_3=3\), \(p_3=0.27\).

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Step3: Sum up the results

\(0.3+0.86 + 0.81=1.97\)

Answer:

\(1.97\)