A certain professor will choose problem for their exam from two possible sources

Question

A certain professor will choose problem for their exam from two possible sources, textbook problems and non textbook problems. There are 15 on the exam, and the number of problems that come from textbook problems is a random variable. The textbook problems on the exam will be randomly chosen from a set of 70 textbook problems and the non textbook problems will be randomly selected from a set of 30 non textbook problems. Calculate the probability that the exam has more than two textbook problems.

Explanation / Answer

There are 70+30 = 100 problems to choose from.

Note that P(more than x) = 1 - P(at most x ).          
          
Using a cumulative hypergeometric distribution table or technology, matching          
          
where          
N = population size =    100      
K = number of successes in the population =    70 textbook problems      
n = sample size =    15      
x = critical number of successes in the sample =    2      
          
Thus,          
P(at most   2   ) =    4.07941E-08

Thus, the probability of at least   1   successes is  
          
P(more than   2   ) =    0.999999959 [ANSWER]

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