Determine the following given the ensuing. A trial entails the flip of three fai

Question

Determine the following given the ensuing.

A trial entails the flip of three fair coins

A success in a trial entails getting other than all heads or all tails on the three coins

12.1 For one trial, frequency table depicting the possible outcomes and related probabilities

12.2 For one trial, expected number of successes and most likely number of successes

12.3 For three trials, probability of 0, 1, and 2 successes in any order

12.4 For three trials, probability of 0, 1, and 2 successes in that order

12.5 For one trial, probability of 0, 1, or 2 successes

12.6 For one trial, probability of success on the 2nd and 3rd flips given an unknown result on the first flip

Explanation / Answer

12.1 For one trial, frequency table depicting the possible outcomes and related probabilities is

12.2 For one trial frequency table depicting the success and related probabilities is

Thus, the expected number of success is = 6 x 6/8 + 2 x 2/8 = 5

12.3   For three trials, probability of 0, 1, and 2 successes in any order is 3 x [(1/2)3 + (1/6)(1/2)2 + (1/6)2(1/2)] = 3 x 0.1806 = 0.5418

12.4 For three trials, probability of 0, 1, and 2 successes in that order is [(1/2)3 + (1/6)(1/2)2 + (1/6)2(1/2)] = 0.1806

12.5 For one trial, probability of 0, 1, or 2 successes are (1/2)3 = 1/8, (1/6)(1/2)2 = 1/24, and (1/6)2(1/2) = 1/72 respectively.

12.6 For one trial, probability of success on the 2nd and 3rd flips given an unknown result on the first flip is (1/6)(1/2) = 1/12, and (1/6)2 = 1/36 respectively.

Possible Outcome Probability (HHH) 1/2 x 1/2 x 1/2 = 1/8 (HHT) 1/2 x 1/2 x 1/2 = 1/8 (HTH) 1/2 x 1/2 x 1/2 = 1/8 (HTT) 1/2 x 1/2 x 1/2 = 1/8 (THH) 1/2 x 1/2 x 1/2 = 1/8 (THT) 1/2 x 1/2 x 1/2 = 1/8 (TTH) 1/2 x 1/2 x 1/2 = 1/8 (TTT) 1/2 x 1/2 x 1/2 = 1/8

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