0.65 0.10 b) Ben post a video on SnapChat claiming the probability of passing th

Question

0.65 0.10 b) Ben post a video on SnapChat claiming the probability of passing this class is 82%, is he correct? Explain your answer? oura).550.13) 881.8 3) Lupus is a medical phenomenon where antibodies that are supposed to attack foreign cells to prevent infections instead see plasma proteins as foreign bodies, leading to a high risk of blood clotting. It is believed that 2%of the population suffer from this disease. The test is98%accurate if a person actually hasthe disease. The test is74% accurate if apersondoes not havethe disease. There is a line from the Fox television show House that is often used after a patient tests positive for lupus: "It's never lupus." Do you think there is truth to this statement? Use appropriate probabilities to support your answer. (10 points)

Explanation / Answer

Probability that a random peson has lupus :: P(L) = 0.02 , P(Lc) = 0.98
Probability that a random person who has lupus tests positive for lupus :: P(T | L) = 0.98
Probability that a random person who does not have lupus tests positive for lupus :: P(T | Lc) = 0.26 ( Since test is 74% accurate)
So, if a person tests positive for lupus, probability that he actually has lupus :: P(L | T) = P(L T) / P(T)
P(L T) = P(L) . P(T | L)
By total law of probability P(T) = P(L).P(T | L) + P(Lc).P(T | Lc)
P(L T) = 0.02 x 0.98 = 0.0196
P(T) = (0.02 x 0.98) + (0.98 x 0.26) = 0.2744
P(L | T) = (0.0196/0.2744) = 0.0714.
So if a person tests positive, probability that he actually has lupus is 0.0714 i.e a 7 % chance, so there indeed is some truth to the statement "It's never lupus."

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