Medical studies have shown that 10 out of 100 adults have heart disease. When a person with heart disease is given an EKG test, a 0.9 probability exists that the test will be positive. When a person without heart disease is given an EKG test, a 0.95 probability exists that the test will be negative. Suppose that a person arrives at an emergency room complaining of chest pains . An EKG test is given to this person.

One test result is often not sufficiently reliable due to false positive and false negative. Suppose this person is given two tests and assume the two test results are independent.

Let random variable Xindicatewhether someone has heart disease and the sample space is {HD =heart disease,ND =no disease}.Let random variable Y be the number of positive tests out of two EKG tests and the sample space is {0,1,2}.

Complete the conditional probability/likelihood table below.Use decimal and do NOT round your answer and use the exact values.

. Given HD Given ND

Y =0

Y = 1

Y = 2

1 1

Complete the joint probability table below.Use decimal and do NOT round your answer and use the exact values.

. X=HD X=ND Marginal

Y=0

Y=1

Y=2

Complete the posterior (conditional) probability table below. Use decimal and ROUND your answer to the nearest hundred thousandth. For example, if the answer is 0.123456789, round it to 0.12346.

. X=HD X=ND

Given Y=0

Given Y=1

Given Y=2