3 Suppose that the probability of exposure to the flu virus during flu season is
ID: 3071749 • Letter: 3
Question
3 Suppose that the probability of exposure to the flu virus during flu season is 0.4. People can get a flu vaccine which prevents the vacci- nated person getting the flu, if exposed, in 75% of cases. People who are not vaccinated get the flu 80% of the time if they are exposed to the virus. It is impossible for a person to get the flu if they are not ex- posed to the virus. Suppose that two friends, Scott and Kevin spenod Hu contact with the season in different places and are not in physical same people. Scott received the flu vaccine but Kevin did not What is the probability that exactly one of these two will get the flu? b) If exactly one of them does get the flu, what is the probability it is Kevin?Explanation / Answer
a) P(exactly one of those will get flu) = P(Scott received flu and Kevin did not) + P(Scott did not receive flu and Kevin did)
= (0.4x0.25)(1 - 0.4x0.8) + (1 - 0.4x0.25)(0.4x0.8)
= 0.068 + 0.288
= 0.356
b) P(Kevin got flu | exactly one of them got flu)
= P(Kevin got flu & exactly one of them got flu)/P(exactly one of them got flu)
= 0.288/0.356
= 0.809
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