Question

the prices of three t - shirt styles are $24, $30, and $36. the probability of choosing a $24 t - shirt is $\frac{1}{6}$. the probability of choosing a $30 t - shirt is $\frac{1}{2}$. the probability of choosing a $36 t - shirt is $\frac{1}{3}$. what is the expected value of a t - shirt? $29 $30 $31 $32

Explanation:

Step1: Recall the formula for expected value

The formula for expected value \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the values and \(p_i\) are the probabilities.

Step2: Substitute the values into the formula

For \(x_1 = 24\), \(p_1=\frac{1}{6}\); \(x_2 = 30\), \(p_2=\frac{1}{2}\); \(x_3 = 36\), \(p_3=\frac{1}{3}\).

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Step3: Calculate the sum

\(4 + 15+12=31\)

Answer:

\(\$31\)