A new medical drug to cure HIV/AIDS has just been developed. The probability that it will cure HIV/AIDS is 0.9 if the patient has HIV/AIDS. The probability that it will cure HIV/AIDS falls to 0.4 if the patient does not have the disease. There is a probability of 0.3 that a person chosen at random from the community has HIV/AIDS. Find the following: i. Probability that a patient is cured of HIV/AIDS [12 Marks) Probability that a person is cured of HIV/AIDS actually had HIV/AIDS. [8 Marks)

A new medical drug to cure HIV/AIDS has just been developed. The probability that it will cure HIV/AIDS is 0.9 if the patient has HIV/AIDS. The probability that it will cure HIV/AIDS falls to 0.4 if the patient does not have the disease. There is a probability of 0.3 that a person chosen at random from the community has HIV/AIDS. Find the following: i. Probability that a patient is cured of HIV/AIDS [12 Marks) Probability that a person is cured of HIV/AIDS actually had HIV/AIDS. [8 Marks)

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