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Among a group 15% speak French, 45% are women, and 20% of the women also speak French.

Q: What percentage are women that don't speak French, what percentage only speak French and not woman?

My thoughts:

(1) Using a venn diagramenter image description here

Let $A = \text{French}$ and $B = \text{Women}$

Since $B = (B \cap A^{c}) \space \cap (B \cap A)$, we have to find $B \cap \overline{B \cap A}$ right?

What is the way? Is the answer $45% - 20% = 25%? But I don't see the manipulation of formulas behind it. Like the way I was trying?

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    Note that the statement "20% of the women speak French" is different from "20% are women and speak French". Your Venn diagram implies the second one. – 2017-01-23
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    So now can you re-do your (very pretty) Venn Diagram so it has the correct percentages in each of the regions? Maybe put a box around it to include the whole group; then what percentage are outside both circles? Also consider this: if it were _50%_ (not 15%) French speakers, do you see that doing it your way would give percentages adding to more than 100%? – 2017-01-23

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To simplify our thinking, let's just say we have a 100 people. We're basically told that 15 of these people speak French and that 45 are women. We're also told that 20% of the women speak French. In other words 1/5 of the women speak French. That is, $45*\frac{1}{5}=9$ women speak French. Let's address the first question: out of the 100 people, how many are non-French speaking women? Well we found that 9 women speak French, so 36 women don't. So out of the 100 people, 36 people are non-French speaking women. So 36%. As for the second question, we established at the start that 15 people speak French. We also know that there are 9 French-speaking women. So we must have 15-9=6 men that speak French. So that gives us 6%.

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    Nice and simple! – 2017-01-23
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$20\%$ of the women speak French means that $20\%\cdot45\%=9\%$ of the group are women who speak French.

So women who don't speak French are $45\%-9\%=36\%$

Speak French and not women are $15\%-9\%=6\%$

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What's wrong is that your Venn Diagram is a bit incorrect.

Since we have 20% of the women speaking French that would be $45\%\cdot 20\%=9\%$ total.

So the amount of women that don't speak French is 36%.

The amount of men that speak French is 6%.