Given the following set of numbers: {4, 16, 64} Following are the hypothesis that could've generated the set of numbers: 1. Random numbers (1 - 100) 2. Even numbers (1 - 100) 3. Powers of 2 (1 - 100)...

R1

Extracted text: Given the following set of numbers: {4, 16, 64} Following are the hypothesis that could've generated the set of numbers: 1. Random numbers (1 - 100) 2. Even numbers (1 - 100) 3. Powers of 2 (1 - 100) 4. Powers of 4(1 - 100) The prior probabilities of the hypotheses are: [0.15, 0.15, 0.65, 0.05] What is the posterior probability to be generated from the powers of 4 hypothesis? (Write your answer as a decimal of at least two decimal places e.g., 8% = 0.08 You are using a probabilistic generative model. 94% of the people in the world don't have cancer. If a person has cancer it is detected in 95% of the tests. What is the probability of a person having cancer given a positive test result? p(C cancer | x) (x = postive test) (Write your answer as a decimal of at least two decimal places e.g., 8% = 0.08