Conditional probability (flu) numerical Is the flu vaccine effective? In a study

Question

Conditional probability (flu) numerical

Is the flu vaccine effective? In a study in 2007-2008 with 1952 participants, 18-49 years, from the community around 4 university campuses in Michigan the participants were administered a flu shot, nasal flu vaccine, and a placebo. The following table shows probabilities of testing positive for flu depending on the type of treatment. What is the probability of testing positive for flu? What is the probability of testing positive for the flu if somebody had received the placebo? What is the probability that somebody had the nasal vaccine and tested positive for flu? If someone had gotten the flu, what is the probability that he or she had received a flu shot? In the tree diagram what is probability p_8?

Explanation / Answer

A. P(positiv flu)=0.014

B. P(B|A)=P(B and A)/P(A) which means A has occured and what is the prob of B

=P(A)*P(B)/P(A)=0.014

C.

P(B|A)=P(B and A)/P(A) which means A has occured and what is the prob of B

=P(A)*P(B)/P(A)=0.029

D.

P(B|A)=P(B and A)/P(A) which means A has occured and what is the prob of B

=P(A)*P(B)/P(A)=0.014

E. answer is P(flu|Placebo)

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