## Answers

(a) | Test | |||||

Positive | Negative | |||||

Gas Problem | Yes | True Positive | False Negative (Type II error) | |||

No | False Positive (Type I error) | True Negative | ||||

Test | ||||||

Positive | Negative | Total | ||||

Gas Problem | Yes | (85/100) * 400 = 340 | 400-340 = 60 | (4/100) * 10000 = 400 | ||

No | 9600 - 8160 = 1440 | (85/100) *9600 = 8160 | 10000 - 400 = 9600 | |||

Total | 1780 | 8220 | 10000 | |||

(b) Probability = 340/1780 = 0.19101 (19.101%) | ||||||

(c) Probability = 60/8220 = 0.007299 (0.730%) |

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