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The probability to catch disease A is 10%. The probability to get diseases B is 17%. The probability to get at least one of the two A or B is 20%.

a) What is the probability to get sick with both A and B?

b) What is the probability to get A or B but not both at the same time?

c) What is the conditional probability to get A given that we know that we have B?

d) Are the two illnesses independent of each other?

My answers:

a.) A union B is 7%

b.) Do not know how to do this one.

c.) I got 7/17

d.) No, since P(A union B) does not equal P(A)P(B)

Can anyone verify these answers and show me what I got wrong and how to do b?

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up vote 1 down vote accepted

For part a), you are correct.

For part b), we can say that the probability of getting "(A or B) but not both at the same time" is P(A or B) - P(both). You know both these quantities: P(A or B) - P(both) = P(A or B) - P(A and B) = 0.2-0.07=0.13.

For part c), you are correct.

For part d), you are correct.

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Oh yea, three out of four! Thank you very muuch maz906 !!! – Q.matin Oct 3 '12 at 4:27

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