Joe has been given a 10 multiplechoice question in his Geogr

Joe has been given a 10 multiple-choice question in his Geography class. Each question has 5 answers, of which only one is correct. Since Joe has not studied for the quiz, he plans in guessing all of the answers. What is the probability that he answers at least one question correctly? 0.107 0.500 0.893 0.656 A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. Find the probability that the shipment is accepted if 5% of the total shipment is defective? 0.924 0.076 0.050 0.025 An experiment consists of rolling a fair die 8 times and recording the number of times a 3 occurs? The usual number of times a 3 occurs is: 1, 2 and 3. 0, 1, and 2. 0, 1, 2, and 3. 2 and 3 only. Sample items are popular in supermarkets. Costumer takes free samples in about 60% of the cases. When 317 costumers are observed, what is the probability that more than 180 will take a sample? 0.8790 0.8665 0.1335 0.1210

Solution

1.

P(at least one correct) = 1 - P(no correct)

= 1 - (1-1/5)^10

= 0.892625818 [ANSWER, OPTION C]

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2.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.05      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.924516326 [ANSWER, OPTION A]

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