56 Fundamentals of Probability and Statisties for Engineering 3. In an experimon

Question

56 Fundamentals of Probability and Statisties for Engineering 3. In an experimont to study the dependence of hyperacidity on carbonated drinking habits, the following data were collected on 180 individuals: Non Moderate Heavy Drinkers Drinkers Drinkers 36 26 30 Hyperacidity 21 48 19 No Hyperacidity Ifionc of these individuals is selecterd at vaniom, ina the prohability a) experiencing hyperacidity, given that the person is a heavy drinker a non drinker, given that the person is experiencing no hyperacidity. If one of these individuals is selected at random, find the probability that the person is b) A system of 4 components is shown in the accompanying figure Components 1 and 2 are connected in series so that the subsystem works if 1 and 2 work. Components 3 and 4 are connected in the same manner and the 2 subsystems are connected in parallel. If the component work or fail independently of one another and if cach work with probability 0.9, what is the probability that the entire system will work? 4. 2 3 14

Explanation / Answer

3)

Follwoing table shows the row total and column total:

a)

Out of 49 heavy drinkers, 30 experience hyperacidity so

P(hyperacidity | heavy drinkers) = 30/49 = 0.6122

b)

Out of 93 persons not experiencing hyperacidity, 48 are non drinkers so

P(non drinkers |not experiencing hyperacidity) = 48/ 93 = 0.5161

Non Drinkers Moderate Drinkers Heavy drinkers Total Hyperacidity 21 36 30 87 No Hyperacidity 48 26 19 93 Total 69 62 49 180

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