PROJECT: VENN DIAGRAMS AND PROBABILITY
Objective: Find probabilities and odds using a Venn Diagram and the
Addition Rule for Probability.
A clinical study of a new, non-drowsy, prescription
medication for allergy relief was tested on 500 patients. The
following table details the adverse effects of this new
medication and the number of patients who experienced
these effects.
Adverse Effects
Headache
Insomnia
Dry Mouth
Drowsiness
Nervousness
Dizziness
Fatigue
Nausea
Sore Throat
Anorexia
Thirst
Sore Throat and Thirst
Fatigue and Headache
Insomnia and Anorexia
Nausea and Dizziness
Nervousness and Dizziness
Nervousness and Nausea
Dry Mouth and Nervousness
Dry Mouth and Headaches
Headaches and Nervousness
Nervousness, Nausea and Dizziness
(c)JupiterImages Corp
Number
15
11
10
7
20
13
11
15
7
7
6
2
3
5
4
3
4
7
4
5
1
Use this table to make a Venn Diagram. Then use the Venn diagram to calculate the
following probabilities and odds. Note: For “OR” problems, count the number of
people within the specified circles.
1. P(Experiencing a Headache)
2. P(Experiencing only a Headache)
3. P(Not experiencing Dry Mouth)
4. Odds in favor of experiencing Dizziness.
5. Odds against experiencing Drowsiness.
6. Odds against experiencing Nausea.
7. P(Experiencing Nervousness AND Nausea)
8. P(Experiencing Nervousness OR Nausea)
9. P(Experiencing a Headache AND becoming Drowsy)
10. P(Experiencing a Headache OR becoming Drowsy)
11. Odds in favor of experiencing an adverse reaction.
12. Odds against experiencing an adverse reaction.
13. P(Experiencing a Headache AND Fatigue AND Dry Mouth)
14. P(Experiencing a Headache OR Fatigue OR Dry Mouth)
15. P(Experiencing Nervousness AND Nausea AND Dizziness)
16. P(Experiencing Nervousness OR Nausea OR Dizziness)
17. Odds against experiencing a Sore Throat AND being Thirsty.
18. Odds in favor of experiencing Nervousness OR Nausea.
19. Odds against experiencing Anorexia OR Fatigue.
20. P(Not experiencing Anorexia AND Fatigue)