# Probability theory problem

Hello, I was hoping somebody can guide me with this problem, or perhaps help walk me through it. Its for a stats (probability theory) class.

-- Suppose that the probability of exposure to the flu virus during flu season is 0.3. People can get a flu vaccine wich prevents the vaccinated person getting the flu, if exposed, in 80% of cases. People who are not vaccinated get the flu 90% of the time if they are exposed to the virus. Suppose that two friends, Scott and Kevin spend flue season in different places and are not in physical contact with the same people. Scott received the flu vaccine but Kevin did not.

a) what is the probability that at least one of these two get the flu?
b) if at least one of the did get the flu, what is the probability it was kevin.

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Yes, this problem is very tricky.

What I initally tired to do was figure out the probability that kevin and scott got the flu, but that didn't work.

I thought of finding A u B where A is the probability that scott go the flue and B the probability that kevin got it. A u B is the probability that at least one of them gets it.

Thanks

HallsofIvy
Homework Helper
Hello, I was hoping somebody can guide me with this problem, or perhaps help walk me through it. Its for a stats (probability theory) class.

-- Suppose that the probability of exposure to the flu virus during flu season is 0.3. People can get a flu vaccine wich prevents the vaccinated person getting the flu, if exposed, in 80% of cases. People who are not vaccinated get the flu 90% of the time if they are exposed to the virus. Suppose that two friends, Scott and Kevin spend flue season in different places and are not in physical contact with the same people. Scott received the flu vaccine but Kevin did not.

a) what is the probability that at least one of these two get the flu?
b) if at least one of the did get the flu, what is the probability it was kevin.

---

Yes, this problem is very tricky.

What I initally tired to do was figure out the probability that kevin and scott got the flu, but that didn't work
I thought of finding A u B where A is the probability that scott go the flue and B the probability that kevin got it. A u B is the probability that at least one of them gets it

Thanks
1) What is the probability that Scott is exposed to the flue? What is the probability that he will get the flue IF he is exposed? Prob(A)= Prob(A given B)*Prob(B).

2) Now answer the same questions for Kevin.

Since, presumably, the probabilities for Keven and Scott are independent (if they "hang around" together that may not be true but then there is no way to do this problem!) the probability they will both get the flu is the probabilities you found in (1) and (2) multiplied together.

The probability of S or K or both get the flue is the probability S gets the flue + probability K gets the flue- probability both get the flue.

so let me try 1. What you are saying is that you have to use the multiplication rule of probability....

S - the event that scott gets the flu.
K - the even that kevin gets the flu.
B - the event that scott/kevin is exposed to the flu.

P(S) = P(S given B) * P(B)
= (0.2)(0.3)
= 0.6

P(K) = P(K given B) * P(B)
= (0.9)(0.3)
= 0.27

The probability that they both get it, thats P(SK) = (0.27)(0.6) = 0.162

1) if at least one of them gets it, thats (S u K) = P(S) + P(K) - P(SK) = 0.168

2) probability that kevin gets the flu is what i stated above, 0.6

Does this sound right?

Thanks again :)