VENN DIAGRAM

Question

A GROUP OF 100 STUDENTS WERE SURVEYED TO FIND WHETHER THEY DRANK TEA, COFFEE OR A SOFT DRINK .

24 HAD NOT DRUNK ANY OF THE THREE

51 DRANK TEA OR COFFEE BUT NOT A SOFT DRINK

41 DRANK TEA

20 DRANK AT LEAST TWO OF THE THREE

8 DRANK TEA AND A SOFT DRINK BUT NOT COFFEE

9 DRANK A SOFT DRINK AND COFFEE

4 DRANK ALL THREE.

 

REPRESENT THE ABOVE INFO.

FIND THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM FROM THE GROUP HAD DRUNK TEA OR COFFEE.

FIND THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM FROM THE GROUP HAD DRUNK TEA AND COFFEE BUT NOT A SOFT DRINK.  THANKS FOR YOUR HELP.

Answer 1

This problem asks you to create a Venn Diagram to represent the survey data. Make three overlapping circles. We'll need to fill in several numbers: students who drank all three (in the center), students who drank only tea and coffee, students who drank only tea and a soft drink, students who drank only coffee and a soft drink, students who drank only tea, students who drank only coffee, students who drank only a soft drink, and students who drank none of the three.

 

 

Let's do this one by one:

 

students who drank none of the three = 24 (you're told this)

 

students who drank all three = 4 (you're told this)

 

students who drank only tea and a soft drink = 8 (you're told this)

 

students who drank only coffee and a soft drink = 5 (9 who drank coffee and a soft drink, as you're told, minus 4 who drank all three)

 

students who drank only tea and coffee = 3 (20 who drank at least two of the three, as you're told, minus 4 who drank all three, minus 8 who drank only tea and a soft drink, minus 5 who drank only coffee and a soft drink)

 

students who drank only tea = 26 (41 who drank tea, as you're told, minus 4 who drank all three, minus 8 who drank only tea and a soft drink, minus 3 who drank only tea and coffee)

 

students who drank only coffee = 22 (51 who drank tea or coffee but not a soft drink, as you're told, minus 26 who drank only tea, minus 3 who drank only tea and coffee)

 

students who drank only a soft drink = 8 (100 students surveyed, as you're told, minus 24 who drank none of the three, minus 26 who drank only tea, minus 22 who drank only coffee, minus 5 who drank only coffee and a soft drink, minus 8 who drank only tea and a soft drink, minus 3 who drank only tea and coffee, minus 4 who drank all three)

 

 

You should finally have the full Venn Diagram completed. You can answer the questions now:

 

Probability of tea or coffee = 26 only tea + 22 only coffee + 3 only tea and coffee + 8 only tea and a soft drink + 5 only coffee and a soft drink + 4 all three = 68 students out of 100 total students = 68/100 = 17/25

 

Probability of tea and coffee but not a soft drink = 3 only tea and coffee = 3 students out of 100 total students = 3/100