Seventeen people have been exposed to a particular disease E

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital\'s capacity will be exceeded? (a) 0.011 (b) 0.035 (c) 0.092 (d) 0.965 (e) 0.989

Solution

The capacity is exceed when at least 11 have the disease.

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 =    17      
p = the probability of a success =    0.4      
x = our critical value of successes =    11      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   10   ) =    0.965187271
          
Thus, the probability of at least   11   successes is  
          
P(at least   11   ) =    0.034812729 = 0.035 [ANSWER, B]