Jessica has a four-sided die, a six-sided die, and a 12-sided die. She rolls the three dice once. Let Z be the number of fours showing. Find E[Z] using the indicator method.

The value of E [Z]  is 0.50.

Step-by-step explanation:

The expected value is computed using the formula:

Denote the three dices as follows:

X₁ = a four-sided die

X₂ = a six-sided die

X₃ = a 12-sided die

Define the indicator variables as follows:

The probability of rolling a 4 in the three dices are as follows:

Compute the value of E [Z] as follows:

Thus, the value of E [Z]  is 0.50.