Heart failures are due to either natural occurrences 86 or o

Heart failures are due to either natural occurrences (86%) or outside factors (14%). Outside factors are related to induced substances (73%) or foreign objects (27%). Natural occurrences are caused by arterial blockage (56%), disease (27%), and infection (e.g., staph infection) (17%). Round your answers to four decimal places (e.g. 98.7654). a) Determine the probability that a failure is due to induced substance. b) Determine the probability that a failure is due to disease or infection.

Solution

a. A failure due to an induced substance occurs 73% of the time WHEN IT IS AN OUTSIDE FACTOR. So to find the probability that a failure is due to an induced substance, we must multiply the probability that it is due to an outside factor by the probability that it is due to an induced substance: P(induced substance) = .13*.73 = .0949. b. The probability that it is due to disease or infections can be found by noting, again, that both of these only occur when it is a natural occurrence. So we add together the probabilities of each multiplied by the probability of natural occurrence: P(disease or infection) = .87*.27 + .87*.17 = .3585. Hope this makes sense!