Last summer my mother and I were in charge of setting up a morning brunch for our family reunion. We set up the brunch to see if those who attended would be interested in both coffee and or juice being served with their brunch. The last reunion showed that the money spent on juice was a lost due to more coffee drinkers. At the brunch buffet, 116 people preferred coffee as a beverage, 32 people preferred juice, 40 preferred both coffee and juice. I needed to find out if each person prefers at least one of the beverages, then how many people would visit the brunch buffet?

Let A = the set of people who prefer coffee
Let B = the set of people who prefer juice.
n(A) = 116, n(B) = 32, n(A ∩ B) = 40
n(AUB) = n(A) + n(B) - n(A ∩ B)
Plugging-in all the values,
n(AUB) =116 + 32 - 40
n(AUB) = 108

Question

Last summer my mother and I were in charge of  setting up a morning brunch for our family reunion. We set up the brunch to see if those who attended would be interested in both coffee and or juice being served with their brunch. The last reunion showed that the money spent on juice was a lost due to more coffee drinkers. At the brunch buffet, 116 people preferred coffee as a beverage, 32 people preferred juice, 40 preferred both coffee and juice. I needed to find out if each person prefers at least one of the beverages, then how many people would visit the brunch buffet?

Let A = the set of people who prefer coffee 
Let B = the set of people who prefer juice.
n(A) = 116, n(B) = 32, n(A ∩ B) = 40
n(AUB) = n(A) + n(B) - n(A ∩ B)
Plugging-in all the values,
n(AUB) =116 + 32 - 40
n(AUB) = 108

anonymous · Answer

Seems rright to me.