Of the 5 assembly lines in a certain plant, 2 do not meet a certain

Question

Of the 5 assembly lines in a certain plant, 2 do not meet a certain safety standard. If 2 of the 5 assembly lines will be randomly selected for inspection, what is the probability that both of the assembly lines selected meet that safety standard?

A. 2/25

B. 1/10

C. 3/10

D. 3/5

E. 11/10

Natashaairan · Answer

3c2/5c2

Favourable by total

Posted from my mobile device

Shreya1211 · Answer

Out of 5 Assembly lines, 2 do not meet a certain safety standard. Then, out of those 5, 3 does meet the safety standard.
Therefore, when 2 out of the 5 lines are randomly selected, possibility that both of the assembly lines selected meet that safety standard = 
  3/5 * 2/4 = 3/10

NOTE (to understand the fundamental behind the above calculation):  
There are 3 lines that does meet the safety standard, so the possibility when randomly selecting the first line that will meet the safety standard is 3/5. Now, as we have selected 1 line out of the 5 total lines, then 4 are remaining, and only 2 will be remaining out of the 3 lines that meet the safety standard. So the possibility of selecting the second line is 2/4

lavanya.18 · Answer

There are two approaches to attempting this question:

1) 3/5 * 2/4 = 3/10 (simple and quick)

But in case you want to use combinations:

2) 3C2/5C2= 3*2/2 / 5*4/2 = 3/10

Danou · Answer

I used method 1, but had initially wanted to use combinations. Can you elaborate on your equation / how you got to the 3/10? Thanks

SwethaReddyL · Answer

Hi  Danou , out of 5, we are selecting 2. So 5C2 for total outcomes; we need to select 2 from the non defect one's. No.of non defect one's are 3, as the question mentioned 2 are defect (5-2=3). Now, just get the solution, Favourable outcome/Total outcome = 3C2/5C2.

Hope this helps.

Of the 5 assembly lines in a certain plant, 2 do not meet a certain

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Of the 5 assembly lines in a certain plant, 2 do not meet a certain

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