Coin Flipping Experiment

Reply #3

Orange71 — Fri, 16 May 2025 15:55:26 GMT

Here is my solution using sets, conditional and Joint probabilities, and Bayes Theorem.

Reply #2

Orange71 — Thu, 15 May 2025 19:05:41 GMT

Tucker, that is the correct answer. Well done.

Reply #1

Tucker Black — Thu, 15 May 2025 17:49:36 GMT

I come up with 0.567.

Probability of four heads and one tail out of five flips is P(head)^4*P(tail)^1*(5 choose 4).

5 choose 4 is 5 (i.e. HHHHT, HHHTH, HHTHH, HTHHH, THHHH).

For coin A, this probability of getting four heads and one tail in any order is 0.4^4*0.6^1*5 = 0.0768, for coin B it is 0.15625, and for coin C it is 0.36015.

The probability of getting a certain coin followed by four heads and one tail is the probability of getting that coin times one of the

Coin Flipping Experiment

Orange71 — Sun, 11 May 2025 23:54:37 GMT

Suppose we a coin flipping experiment with the following rules. First, one of three coins is chosen randomly with probabilities P(Coin A) = 0.5, P(Coin B) = 0.3, and P(Coin C) = 0.2. After the coin is selected in the first step (but we are not told which one), the same coin is flipped five times, each time with a random result of Head or Tail with probabilities as shown in the diagram, with each flip independent of all the other flips. We are told the result is 4 Head and 1 Tail (but not which o... [ More ]