The Joe Bud. 2018 Goldman Sachs Engineering Math 54m : 30s to test end A mod fie

Question

The Joe Bud. 2018 Goldman Sachs Engineering Math 54m : 30s to test end A mod fied gene occurs with probability of 0.5% in the population. There 's a test for the mod fied gene. If a gene s modified, the test always returns a postive. If the gene is not modified, the test returns a false positive 7% of the time. A random gene is tested, and it returns a positive What is the probability that the gene is modifie rounded to three decimal places? Pick one of the choices 0.035% o 6.667% o 6.698% None of the above Clear selection Probability and Statistics-Meeting and meet sometime between 7 PM and 8 PM. They decide that whoever arrives first will wait 10 minutes for the other person if the other person waiting will leave, What is the probability that they will meet? Assume uniform distribution for arrival time between 7 rson doesn't turn up inside 10 minutes, the PM and 8 PM for both of them. Pick one of the choices 11/36 O1/2 5/9 None of the Above.

Explanation / Answer

Solution:

Given that Gene modified & returns positive = 0.005
gene not modied & returns positive = 1-0.005
probability that test is positive = P( gene modified & returns positive+gene not modied & returns positive)

= 0.005*1+(1-0.005)*0.07 =0.07465

hence probability that gene is modified given test positive = 0.005*1/0.07465
= 0.066979 ~ 6.698 %

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