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

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Basic Math

Confounding

Problem 17

In the popular TV cartoon series, "The Simpsons," the Simpsonfamily 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 anddonuts. Suppose that Marge is in the room 20% of the time that Bartis eating chips and 50% of the time that Bart is eating donuts.Similarly, suppose that Marge is in the room 20% of the time thatHomer is eating chips and 50% of the time that Homer is eatingdonuts; thus she catches them eating each kind of snack equallyoften. Nonetheless, Marge is in the room 32% of the time that Bartis eating either donuts or chips, and Marge is in the room 41% ofthe time that Homer is eating either donuts or chips. Suppose thatHomer and Bart never eat chips and donuts in the same snack--eatingchips and eating donuts are mutually exclusive.

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

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

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