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In a company are 100 workers.

  • 50 of them (100) speak ENG
  • 30 of them (100) speak GER
  • 15 of them (100) speak ENG and GER

What is the probability of randomly selected worker speaks GER on condition he does NOT speaks ENG?

I have two suggestions:

  • a) 3/10
  • b) lower than 3/10
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  • $\begingroup$ Wouldn't the probability just be 1/2 of GER/TOTAL since half of the workers speak english? $\endgroup$ – David Greydanus Jun 6 '15 at 17:47
  • $\begingroup$ only 30 of 100 workers speak GER so without the ENG condition it would be 3/10 so I believe it shold be lower :) $\endgroup$ – Luxqs Jun 6 '15 at 17:52
  • $\begingroup$ Are speaking ENG and GER independent? I would be illogical if it was so, but without assuming that we can't solve the problem. $\endgroup$ – wythagoras Jun 7 '15 at 7:22
  • $\begingroup$ Sorry now I see my mistake, update in a minute. $\endgroup$ – Luxqs Jun 7 '15 at 7:29
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As described in the problem, a worker speaking German and a worker speaking English are independent events. As such, the fact that a worker speaks English doesn't actually give you any information as to whether or not a worker speaks German. Thus, the odds that a worker speaks German given that he speaks English is the same as the odds that a worker speaks German: $\frac{3}{10}$

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  • $\begingroup$ I think by "on condition he does speaks ENG" means the worker must speak both GER and ENG, but the question is ambiguous. $\endgroup$ – David Greydanus Jun 6 '15 at 17:52
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Speaks GER but no ENG = 15
divided by
no ENG speaking people 50.

15 / 50 = 0.3

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-1
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ENG          Non-ENG
☺☺☺☺☺☺☺☺☺☺ | ☺☺☺☺☺☺☺☺☺☺
☺☺☺☺☺☺☺☺☺☺ | ☺☺☺☺☺☺☺☺☺☺
☺☺☺☺☺☺☺☺☺☺ | ☺☺☺☺☺☺☺☺☺☺
☻☻☻☻☻☺☺☺☺☺ | ☻☻☻☻☻☺☺☺☺☺
☻☻☻☻☻☻☻☻☻☻ | ☻☻☻☻☻☻☻☻☻☻

☻ = GER

The odds of randomly selecting a GER speaker out of the total are $3/10$ (30 GER out of 100 workers) and half of the workers also speak ENG.

Therefore, the odds of a randomly selected worker speaking GER and not ENG are $1/2$(Fraction of workers that don't speak ENG) times 3/10(fraction of workers that speak GER).

$.15$ or $3/20$

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  • $\begingroup$ sorry my mistake, he does NOT speak ENG. But maybe in this case it does not matters :) 50:50 $\endgroup$ – Luxqs Jun 6 '15 at 18:00
  • $\begingroup$ @Luxqs Same odds then since the number of ENG speakers = Number of non-ENG speakers. $\endgroup$ – David Greydanus Jun 6 '15 at 18:01
  • $\begingroup$ @Luxqs See the graph I made, the groups are the same. $\endgroup$ – David Greydanus Jun 6 '15 at 18:02
  • $\begingroup$ can you more deeper write how you get the number like my error calculation ((15/100)/(50/100)) $\endgroup$ – Luxqs Jun 6 '15 at 18:04
  • $\begingroup$ By your own chart, the answer is 0.3... the question is what is the odds of a black smiley face in the right group. That's 15/50... -1. $\endgroup$ – Barry Jun 6 '15 at 19:03

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