A manufacturer produces soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 12% of the cans are defective. What is the probability that the two selected cans are defective if the quality control worker selects the two cans from a batch of 50 cans?
A) 3/245
B) 3/250
C) 9/625
D) 6/35
Also how did you get the answer?
It depends. If the selection is made WITHOUT REPLACEMENT, then the probability of the first can is 12% = 12 out of 100 = 6 out of 50 = 3/25. The probability of the 2nd can is then 5 out of 49 (assuming the first can is bad). We multiply the two separate probabilities to get the probability of the two events together: (3/25) * (5/49) = (3/245) = Answer "A".
But nothing says that the control worker couldn't make the selection WITH REPLACEMENT. If so, then the probability of the first can is 12/100, and the probabilty of the 2nd can is also 12/100. The two events together is (12/100) * (12/100) = (9/625) = Answer "C".
