A food scientist is developing a new recipe. He needs it to have between 3 and 5 teaspoons of sugar per serving and between 3 an
d 6 grams of fiber. Each teaspoon of sugar has 5 carbohydrates. Each gram of fiber counts as a carbohydrate when counting total carbohydrates. If the recipe already has 10 carbohydrates per serving from other sources, create a linear programming feasible region to minimize the total carbohydrates in the recipes nutrition profile.
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1. B and Y are 2 events,and Y has already occurred.
2. P(B|Y)=P(B∩Y)/P(Y),
gives the probability of B to occur, once Y has already happened.
3. According to the givens (check the diagram at the bottom, of the described problem),
P(B∩Y)=n(B∩Y)/n(U)=8/26=4/13
P(Y)=n(Y)/n(U)=12/26=6/13
P(B|Y)=P(B∩Y)/P(Y)=(4/13)/(6/13)=4/6=2/3=0.67
2. P(B|Y)=P(B∩Y)/P(Y),
gives the probability of B to occur, once Y has already happened.
3. According to the givens (check the diagram at the bottom, of the described problem),
P(B∩Y)=n(B∩Y)/n(U)=8/26=4/13
P(Y)=n(Y)/n(U)=12/26=6/13
P(B|Y)=P(B∩Y)/P(Y)=(4/13)/(6/13)=4/6=2/3=0.67