Answer:
a)Smoke but doesn't drink alcoholic beverages
P=0.176 or 17.6%
b)eats between meals and drinks alcoholic beverages but doesn't smoke
P=0.062 or 6.2%
c.) neither smokes nor eats between meals
P=0.342 or 34.2%
Step-by-step explanation:
Using a Venn diagram with three circles, one for each bad health habit. Let us 
for the students that only smoke, 
for only drink alcoholic beverages, and 
for only eat between meals. Following this logic, 
represents smoke and drink alcoholic beverages but not eat between meals, 
drink alcoholic beverages and eat between meals but not smoke,
eat between meals and smoke but not drink alcoholic beverages. Finally 
for having all the three, this means 
.
To find , subtract 52 (the three problems) from 97 because this last number represents all the students that smoke and eat between meals, including the students that have the three bad habits. The same goes for 'd' and 'e'.
To find , subtract , , and from the total of smokers. This is because , , and represent smoke and at least another bad habit and represents only smoking.
The same goes for and .
Adding all letters and subtract from the total to see if there is any healthy student:
a)Smoke but doesn't drink alcoholic beverages
This will be 'a' (only smokes) and 'f' ( smokes and eats between meals but doesn't drink) divided by the total of students.
b)eats between meals and drinks alcoholic beverages but doesn't smoke
This probability is 'e' divided by the total of students.
c.) neither smokes nor eats between meals
This will be 'b' (only drinks) plus the healthy students (66) divided by the total of students.
