No calculat into a calculator to get the final answer, do NOT simplify further o

Question

No calculat into a calculator to get the final answer, do NOT simplify further ors are allowed. Once you get your answer to something that could be plugged 1) (3 points) Suppose that A and B are independent events, such that P(A) = 0.2 and P (B) = 0.4. What is the probability that both A and B happen? 2) (7 points) 1 in 5000 humans have a certain rare mutation. The test for detecting this mutation is accurate (ie, correct) 97% of the time. A person tests positive for the rare mutation. What is the probability that this person actually has the mutation? Hint: The test for detecting the mutation is correct 97% of the time. This means that if the person has the mutation, the test detects it 97% of the time, and if the person does not have the mutation, the test does not detect it 97% of the time (so the test falsely detects it 3% of the time)

Explanation / Answer

(1) P(A and B)=P(A)P(B)=0.2*0.4

=0.8

(2) the test for detecting mutation is 97% correct that is

P(Mc)=0.97

given that A person has mutation means test is correct and it is also given that out of 5000 person only 1 has mutation so,

probability is=1/5000*0.97

=0.000194

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