SIMPSONS PARADOX a) There are two crimson jars (labeled C1 and C2) and two mauve jars (labeled M1 and M2). Each jar contains a mixture of green gummi bears and red gummi bears. Show by example that it...

SIMPSONS PARADOX
a) There are two crimson jars (labeled C1 and C2) and two mauve jars (labeled M1 and M2). Each jar contains a mixture of green gummi bears and red gummi bears. Show by example that it is possible that C1 has a much higher percentage of green gummi bears than M1, and C2 has a much higher percentage of green gummi bears than M2, yet if the contents of C1 and C2 are merged into a new jar and likewise for M1 and M2, then the combination of C1 and C2 has a lower percentage of green gummi bears than the combination of M1 and M2. (b) Explain how (a) relates to Simpson’s paradox, both intuitively and by explicitly de?ning events A,B,C as in the statement of Simpson’s paradox.