SOLUTION: Are 50 iPads available for check out as library, 10 are defective. A sample of 3 iPad Are randomly selected without replacement. What is the probability that at least one of the iP

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Question 1159141: Are 50 iPads available for check out as library, 10 are defective. A sample of 3 iPad Are randomly selected without replacement. What is the probability that at least one of the iPad is defective? round to the nearest thousand
Answer by ikleyn(52944) About Me  (Show Source):
You can put this solution on YOUR website!
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There are 50 iPads available for check. Of them, 10 are defective.
A sample of 3 iPads is randomly selected without replacement.
What is the probability that at least one of the iPads is defective?
round to the nearest thousand
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I edited the original text to make it grammatically correct.
Also,  I removed all the words that are irrelevant,  to transform
from the  " bla-bla-bla "  style to normal mathematical style.


- - - - - - - - S o l u t i o n   1 - - - - - - - -

An event "At least one is defective" is the complement to the event "No one is defective".

An event "No one is defective" means that our 3 randomly selected iPads are from the set 
of 50-10 = 40 good iPads.


So, we write

    P(at least one is defective = 1 - P(no one is defective) = 1 - %2840%2F50%29%2A%2839%2F49%29%2A%2838%2F48%29 = 0.496 (rounded).


At this point, the solution 1 is complete.  The answer is  P = 0.496  (rounded).



- - - - - - - - S o l u t i o n   2 - - - - - - - -

An event "At least one is defective" is the complement to the event "No one is defective".

An event "No one is defective" means that our 3 randomly selected iPads are from the set 
of 50-10 = 40 good iPads.


So, we write

    P(at least one is defective = 1 - P(no one is defective) = 1 - C%2840%2C3%29%2FC%2850%2C3%29 = 1 - 9880%2F19600 = 0.496 (rounded).


Here we relate  C(40,3) = 9880 triples (combinations), consisting of good iPads only, 
to C(50,3) = 19600, the number of all possible triples (combinations).


At this point, the solution 2 is complete.  The answer is  the same:  P = 0.496  (rounded).

Solved completely in two different ways for your better understanding.