Students and sports
100 students in a class are taking part in at least one sport from baseball, soccer and tennis. 8 of them play all three where 6 are interested only in soccer. 56 students do not play soccer where 40 of them involve in exactly two of these. Taking 0 to 100 as the scale, what is the probability of a randomly chosen student playing either baseball or tennis?
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1 solution
Only B=x
Only S=6
Only T=z
B&T=y
B&S=m
S&T=n
All=8
Not S=x+y+z=56
Exactly two=m+n+y=40
→x+2y+z+m+n=96
Also, x+y+z+m+n+8+6=100
So, y=10
x+z=46=required probability