200 students attend a school which offers French and History. 10% of those who take History also take French and 4 times as many students take History as take French. 8% of the students take neither History or French. By drawing a Venn Diagram find the probabilty that a student picked at random does History and French. Give your answer as a percentage.

To find the required probability we have to know what is the number of students that take both History and French ( Intersection of 2 circles in Venn diagram)

1. Lets find the number of students that take History or French or both.

We know that 8% from 200 take neither History or French. So number or students who take History or French or both is 200-200*0.08=184

2. Let number of students that takes French (or both Fr+Hist)=x (left circle)

So number of students that takes History (or both Fr+Hist)=4x (right circle)

So number of students that take both French+History= 10% from 4x or

0.1*4x=0.4x (circles' intersection)

3. Now we have the equation as follows:

x+4*x-0.4*x = 184

4.6*x=184

x=40 students takes French (or both French+ History)

4*x= 40*4=160 students takes History (or both French+ History)

10% from 160 =0.1*160=16 students takes both History and French

P(hist& french)=16/200=0.08