It has been observed that 20% of the examinees on a driving test fail. a.) Assum

Question

It has been observed that 20% of the examinees on a driving test fail. a.) Assume people take the exam one at a time. What is the exact probability that the third person is the first to fail. b.) 50 people take the exam. What is the approximate probability that 7 or more of them fail. It has been observed that 20% of the examinees on a driving test fail. a.) Assume people take the exam one at a time. What is the exact probability that the third person is the first to fail. b.) 50 people take the exam. What is the approximate probability that 7 or more of them fail. a.) Assume people take the exam one at a time. What is the exact probability that the third person is the first to fail. b.) 50 people take the exam. What is the approximate probability that 7 or more of them fail.

Explanation / Answer

A)

P(pass,pass,fail) = (1-0.20)*(1-0.20)*0.20 = 0.128 [ANSWER]

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b)

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 =    50      
p = the probability of a success =    0.2      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.103398227
          
Thus, the probability of at least   7   successes is  
          
P(at least   7   ) =    0.896601773 [ANSWER]

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