Answer:
23
Step-by-step explanation:
The expected value is given by:
[tex]E(X)=\bar X=\sum x\cdot P(x)[/tex]
We have that the probability of choosing a dessert of 16 grams of fat is [tex]\frac{1}{4}[/tex]
We have that the probability of choosing a dessert of 24 grams of fat is [tex]\frac{7}{12}[/tex]
We have that the probability of choosing a dessert of 30 grams of fat is [tex]\frac{1}{6}[/tex]
The expected value is
[tex]E(X)=16*\frac{1}{4}+24*\frac{7}{12} +30*\frac{1}{6}[/tex]
[tex]E(X)=4+14 +5[/tex]
[tex]E(X)=23[/tex]
