Homework SourseDetermine the following given the ensuing A trial entails th
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
Solution
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 |
