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Bunuel
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Leave out the two defective bulbs;
18C2/20C2=153/190

or

Deduct the case of “one defective+one non-defective” and “both defective”;
(20C2-18C1*2C1-2C2)/20C2=(190-36-1)/190=153/190
(The formar solution is way simpler)

D is the answer

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Bunuel

I'm trying to solve this question using the complement method. P(defective) = 1 - P(NOT defective)

P(defective) = 2/20 * 1/19 = 1/190

Inserting in formula :

1/190 = 1 - P(NOT defective)
P(Not defective) = 189/190

What is wrong with this approach?
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Arif27437
Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?

A. 37/190
B. 17/19
C. 9/10
D. 153/190
E. 189/190


Bunuel

I'm trying to solve this question using the complement method. P(defective) = 1 - P(NOT defective)

P(defective) = 2/20 * 1/19 = 1/190

Inserting in formula :

1/190 = 1 - P(NOT defective)
P(Not defective) = 189/190

What is wrong with this approach?
The opposite event of (Not defective, Not defective) is not (Defective, Defective) it's (Not defective, Defective) + (Defective, Not defective) + (Defective, Defective).

P(Not defective, Not defective) =

= 1 - (P(Not defective, Defective) + P(Defective, Not defective) + P(Defective, Defective)) =

= 1 - (18/20*2/19 + 2/20*18/19 + 2/20*1/19) =

= 153/190

Answer: D.

Hope it helps.­
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Bunuel, how the problem should be rephrased, so we can use the following formula to select 2 non defective lightbulb from 18 lightbulbs:
2/18=1/9
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