The question below is a Bayesian statistical question, so you should treat it as

Question

The question below is a Bayesian statistical question, so you should treat it as one. Thanks

1) . One of my prized possessions is my 'simplifed quantum coin', described by P(X =
     P(X =1 | p ) = p, P(X = 0 | p) = 1 - p, where X is the number of heads in a toss of the coin, and p is a random variable with P(p = 1/4) = 1/4 and P(p = 3/4) = 3/4.
(a) What is the probability of a 'head' in a single toss of this coin?
(b) If the coin is tossed and a 'head' results, what is the probability that p is
      3/4?

Explanation / Answer

One of my prized possessions is my 'simplifed quantum coin', described by

P(X = P(X =1 | p ) = p, P(X = 0 | p) = 1 - p, where X is the number of heads in a toss of the coin,

and p is a random variable with P(p = 1/4) = 1/4 and P(p = 3/4) = 3/4.

(a) What is the probability of a 'head' in a single toss of this coin?

Single coin has two outcomes head and tail.

head has probability 1/2.

and tail has probability 1/2.

The probability of a 'head' in a single toss of this coin 1/2.

(b) If the coin is tossed and a 'head' results, what is the probability that p is 3/4?

P(p=3/4) = 3/4

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