A box of 200 printer cartridges is used to stock theshelves. 15 of the cartridge
ID: 3090675 • Letter: A
Question
A box of 200 printer cartridges is used to stock theshelves. 15 of the cartridges are defective. i) A customer buys 10 cartridges from the 200. What isthe probability that all the ones be bought are good? ii) A second customer buys 10 more cartridges from the sameshelf. What is the probability that he got all good ones too,assuming the first customer got all good ones? A box of 200 printer cartridges is used to stock theshelves. 15 of the cartridges are defective. i) A customer buys 10 cartridges from the 200. What isthe probability that all the ones be bought are good? ii) A second customer buys 10 more cartridges from the sameshelf. What is the probability that he got all good ones too,assuming the first customer got all good ones?Explanation / Answer
Analysis: -The box contains 200 catridges where 15 are defective (thismeans 15 out of 200 catridges are defective and the other 185 catridges [200-15=185] are good) -I will state the answer in both a percentage and afraction Solution: -Part (i) -A customer buys 10 out the 200 catridges available where15 of them are defective -This means the other 185 out the 200 catridges are goodso.. his chances of getting good catridges is 185 out of 200the answer is (185/200) reduces to --> (37/40) -to convert this answer to a percentage you divide thenumerator by the denominator and multiply by 100 so.. -37/40 x 100 is 92.5% so the customer has a 92.5% chance of getting 10 good catridges -Part (ii) -If the first customer got all the good ones that means the 15defective catridges are still on the shelf -So now there is only 190 catridges because the first customerbought ten yet there is still 15 defective ones -The chance of getting a defective catridge now is (15/190)instead of (15/200) -So the new chances of getting a good catridge is (175/190) because [190-15=175] reduces to -->(35/38) -the percentage is 35/38 x 100 = 92.1053% or round to 92.1% chance of the second customer gettingall good catridges Accuracy: the second answer should be less than thefirst one because 10 good catridges were boughtalready by the first customer giving the second customer lesschance of getting all good catridges (I hope my reasoningmakes sense to you) catridges Accuracy: the second answer should be less than thefirst one because 10 good catridges were boughtalready by the first customer giving the second customer lesschance of getting all good catridges (I hope my reasoningmakes sense to you)Related Questions
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