Heart failure is due to either natural occurrences (87%) or outside factors (13%

Question

Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Suppose that 20 patients will visit an emergency room with heart failure. Assume that causes of heart failure. Assume that causes of heart failure for the individuals are independent. What is the probability that three or more individuals have conditions caused by outside factors? 0.342 0.792 0.272 0.492

Explanation / Answer

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.13      
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   2   ) =    0.507957787
          
Thus, the probability of at least   3   successes is  
          
P(at least   3   ) =    0.492042213 = 0.492 [ANSWER, D]

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