The probability that Chloe is happy given that she has had dinner by $6 \mathrm{pm} $ is $0.9 $ The probability that Chloe is not happy given that she has not had dinner by $6 \mathrm{pm) $ is $0.8$. Assume that there is a $60 %$ chance that Chloe eats dinner by $6 \mathrm{pm} $ on a given day. a) If Chloe is not happy at $6 \mathrm{pm} $, find the probability that she has not had dinner yet. b) If Chloe is happy at $6 \mathrm{pm} $, find the probability that she has already had dinner. Exercise 2 Find a value $\mathbf {C}$ such that $$ \iint_{A} C X^{3} y^{2} d x d y=1 $$ where $A=\{(x, y): 0