What is probability of language knowledge in company? [closed]

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
• Wouldn't the probability just be 1/2 of GER/TOTAL since half of the workers speak english? – David Greydanus Jun 6 '15 at 17:47
• only 30 of 100 workers speak GER so without the ENG condition it would be 3/10 so I believe it shold be lower :) – Luxqs Jun 6 '15 at 17:52
• Are speaking ENG and GER independent? I would be illogical if it was so, but without assuming that we can't solve the problem. – wythagoras Jun 7 '15 at 7:22
• Sorry now I see my mistake, update in a minute. – Luxqs Jun 7 '15 at 7:29

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: $\frac{3}{10}$

• I think by "on condition he does speaks ENG" means the worker must speak both GER and ENG, but the question is ambiguous. – David Greydanus Jun 6 '15 at 17:52

Speaks GER but no ENG = 15
divided by
no ENG speaking people 50.

15 / 50 = 0.3

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 $3/20$

• sorry my mistake, he does NOT speak ENG. But maybe in this case it does not matters :) 50:50 – Luxqs Jun 6 '15 at 18:00
• @Luxqs Same odds then since the number of ENG speakers = Number of non-ENG speakers. – David Greydanus Jun 6 '15 at 18:01
• @Luxqs See the graph I made, the groups are the same. – David Greydanus Jun 6 '15 at 18:02
• can you more deeper write how you get the number like my error calculation ((15/100)/(50/100)) – Luxqs Jun 6 '15 at 18:04
• 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. – Barry Jun 6 '15 at 19:03