Confounding Problem 17 In the popular TV cartoon series, "The Simpsons," the Simpson family has five...

Confounding

Problem 17

In the popular TV cartoon series, "The Simpsons," the Simpson family has five members: Homer, Marge, Bart, Lisa, and Maggie. Let's involve the Simpsons in Simpson's Paradox.

Consider Homer and Bart's consumption of potato chips and donuts. Suppose that Marge is in the room 20% of the time that Bart is eating chips and 50% of the time that Bart is eating donuts. Similarly, suppose that Marge is in the room 20% of the time that Homer is eating chips and 50% of the time that Homer is eating donuts; thus she catches them eating each kind of snack equally often. Nonetheless, Marge is in the room 32% of the time that Bart is eating either donuts or chips, and Marge is in the room 41% of the time that Homer is eating either donuts or chips. Suppose that Homer and Bart never eat chips and donuts in the same snack--eating chips and eating donuts are mutually exclusive.

a) What fraction of the time that Bart eats either chips or donuts does he eat donuts? ______

b) What fraction of the time that Homer eats either chips or donuts does he eat donuts? ______

Expert Solution

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