TREE DIAGRAMS EXAMPLE 24: This was an exam question for using trees for probabil

Question

TREE DIAGRAMS EXAMPLE 24: This was an exam question for using trees for probability A certain virus infects 1 % of people A test used to detect the virus can give a positive result or a negative result. The test results are · positive 80% of the time IF the person has the virus · positive 5% of the time IF the person does not have the virus V event that a person has the virus Pos- event that the test is positive Neg- event that the test is negative Do ALL of the following: (a) Fill in all probabilities along the branches of the tree. (b) Find and write the event and probability corresponding to each complete path through the tree. (c) Find the probability a person's test result is positive. Show your work. Round all probabilities to 3 decimal places (thousandths) V' Pos Neg Pos eg

Explanation / Answer

Ans:

a)Given that

P(V)=0.01

P(V')=1-0.01=0.99

P(pos/V)=0.8

so,P(neg/V)=1-0.8=0.2

P(pos/V')=0.05

so,P(neg/V')=1-0.05=0.95

b)Probability that the test is positive given that person has the virus=P(pos/V)=0.8

Probabilty that the test is positive given that person do not have virus=P(pos/V')=0.05

c)Now,we have to find:

P(pos)=P(pos/V)*P(V)+P(pos/V')*P(V')

=0.8*0.01+0.05*0.99=0.0575

P(V/pos)=P(pos/V)*P(V)/P(pos)=0.8*0.01/0.0575=0.139

P(V'/pos)=1-0.139=0.861

P(V/neg)=P(neg/V)*P(V)/P(neg)=0.2*0.01/(1-0.0575)=0.002

P(V'/neg)=1-0.002=0.998

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.