Question

In my pocket there are two coins. coin 1 is a fair coin, so the probability P(H = 1 | c = 1) of getting heads is 0.5 and the likelihood P(H = 0 | c = 1) of getting tails is also 0.5. coin 2 is biased, so the probability P(H = 1 | c = 2) of getting heads is 0.8 and the probability P(H = 0 | c = 2) of getting tails is 0.2. i reach into my pocket and draw one of the coins at random. i assume there is an equal chance i might have picked either coin. then i flip that coin and observe a head. think about the bayesian framework and describe what is the prior, what is the likelihood in this case.

Answer 1

The prior is the initial probability of picking either coin, with an equal chance for each. The likelihood is the probability of observing a head given the selected coin. For coin 1, the likelihood is 0.5, and for coin 2 it is 0.8.

Step-by-step explanation:

In this case, the prior refers to the initial probability of picking either coin. Since we assume there is an equal chance of picking either coin, the prior probability of selecting coin 1 is 0.5 and the prior probability of selecting coin 2 is also 0.5. The likelihood refers to the probability of observing a head given the selected coin. For coin 1, the likelihood is 0.5 since it is a fair coin and the probability of getting a head is 0.5. For coin 2, the likelihood is 0.8 since it is biased and the probability of getting a head is 0.8.