A-Level Maths: M1-07 [Probability: A Trickier Venn Diagram Problem]

[a.]

I've never come across a teacher that explains as well as you do!

[Masowe.]

who knew that statistics is fun like this. Thank you sir

[connorofarrell]

Hi sir. When answering this I used a different method involving simultaneous equations and was wondering if that would still get correct method marks in an exam?

I started off by labelling the triple intersection as 0.05, and then labelled the other regions as x, b and c. I then came up with the equations:
x+b+0.05=0.9
x+c+0.05=0.7
x+b+c+0.05=1

I solved these to get the same probabilities you got when you drew the diagram in the video. Would this still achieve method marks, and do you think it would work for other Venn diagram questions?

(x=probability of French union German, c=probability of German union Spanish, and b=probability of French union Spanish. Thanks!

[lukeollerhead]

If someone said "90% of students study French and 70% study German pick one at random, what is the probability they study both?" Id be very tempted to multiply 0.9 by 0.7 and id get 63% not 60% as per the Venn diagram. Can you help unpick my logic error?