I have to understand and explain a kinda complicated math problem for a math fair coming up next week. It goes more or less like this (translated from Spanish):
"$100$ people were asked about their preferences when playing sports. Of these, $50$ people played soccer, $40$ people played basketball, and $30$ people rode bikes. Also, $25$ people played both soccer and basketball, $15$ played soccer and rode bikes, and $12$ played basketball and rode bikes. Finally, only $5$ people played all three sports. The rest either didn't know or didn't answer."
a) Represent the proper Venn diagram for this problem.
b) Calculate the following probabilities: $P(\text{play soccer}), P(\text{play soccer and basketball}), P(\text{only ride bikes}), P(\text{do all three sports}), P(\text{does any of the sports}), P(\text{does none of these sports}).$
What I need to figure out is how I would go about finding the answer to this problem and also explaining it mathematically and visually to a bunch of bystanders. Does anybody have some tips or some guidelines to get my on my way?
In this draw three cicrcles intersecting each other. Then start by filling the intersection of all three circle with 5.
25 played soccer and basketball. 5 out of them comes under intersection of all three. So now 20 left with soccer and basketball only.
10 for soccer and rode bikes only.
7 for basketball and rode bikes only.
We filled all intersections now.
People playing only basketball = 40 - Intersections in which basketball comes.
= 40 - ( 5 + 20 + 7 ) = 8
Similarly for only soccer and only rode bikes. You have Venn diagram.