Basic Statistics
posted by Claire corquette .
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 30% 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 30% 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 38% of the time that Bart is eating either donuts or chips, and Marge is in the room 42% of the time that Homer is eating either donuts or chips. Suppose that Homer and Bart never eat chips and donuts in the same snackeating chips and eating donuts are mutually exclusive.
What fraction of the time that Bart eats either chips or donuts does he eat donuts?
What fraction of the time that Homer eats either chips or donuts does he eat donuts?

To standardize data for a z test, you first subtract the _____ from each term in a data set.
a)Mean b)median c) Mode 
Notation:
M  Marge is in the room
C  Bart eats chips
D  Bart eats donuts.
Each probability is conditional on Bart eating either chips or donuts.
P(M) = P(M\C)P(C) + P(M\D)P(D).
rearranging the equation to solve for P(D), you get:
P(D) = [P(M)P(M\C)P(C)]/P(M\D)
So
We don't know what P(C) is, but we do know that it is the complement of P(D), so instead of P(C) write 1P(D)
P(D) = [.46  .40(1P(D))]/.60
First step: (Distribute .40)
P(D) = [.46  .40 + .40P(D)] / .60
Next step, combine like terms (.46.40)
P(D) = [.06 + .40P(D)] / .60
Now write .06 and .40P(D) each as its own separate fraction over .60
P(D) = .06/.60 + .40P(D)/ .60
Step #4  Simplify the fractions
P(D) = 1/10 + 2/3P(D)
Step #5  sub 2/3P(D) from both sides)
1/3 P(D) = 1/10
Final step  mult both sides by 3)
P(D) = 3/10.
That's Bart. Doing the equation a similar way for homer will get you:
P(D) = [.54  .40(1P(D))]/.60
P(D) = [.54  .40 + .40P(D)] / .60
P(D) = [.14 + .40P(D)] / .60
P(D) = .14/.60 + .40P(D)/ .60
P(D) = 7/30 + 2/3P(D)
1/3 P(D) = 7/30
P(D) = 21/30, or in simplest form, 7/10.
Respond to this Question
Similar Questions

french
is this correct? Ashlee Simpson est la femme de Pete Wentz. Homer et Marge sont les parents de Maggie. Miley est la fille de Billy Ray. Kevin Jonas est le frere de Nick. would i use any forms of de (du, de la, de l', des) for any of 
The Simpsons
I don't have DVDs of simpsons shows from Season 10, and I can't watch the full episode on YouTube. Is there a website that has the descriptions of the entire Simpsons family and their satirical characteristics throughout the Episode, … 
Social studies
Describe attitude of George Simpson and his wife towards natives peoples and Metis. how were their views racist? 
calculus
In February, 2002, each episode of "Becker" was typically seen in 8.3 million homes, while each episode of "The Simpsons" was seen in 7.5 million homes. Your marketing services firm has been hired to promote Bald No More, Inc.'s, hair … 
math
Homer was very generous with his bag of jelly bellys. He gave 2/5 of the whole bag to marge and 1/3 of the whole bag to lisa. he then gave 44 of them to bart and discovered that his bag was empty. how many jelly bellys did homer have … 
physics please help
black bart and wyatt earp have a race. wyatt moseys 400m in 58.0s and bart moseys the same distance in 60.0s. by what Distance does wyatt beat bart in this race? 
Statistics
I have been working on the following homework problem: Consider Homer and Bart's consumption of potato chips and donuts. Suppose that Marge is in the room 30% of the time that Bart is eating chips and 40% of the time that Bart is eating … 
science!
this question is not a question but 20 questions. i appreciate if you review all my answers, but i wont provide an answer for the last question (most probably since i didn't finish answering it or typing it out since i only have an … 
Math help
Formulate a linear programming problem for the following situation. Homer Simpson has created two donut assortments for the the Springfield donut shop. The bargain assortment includes 4 pink frosted and 8 glazed donuts and the deluxe … 
Math Word Problems
Bart, Lisa and Maggie went to the "Integers Only Really Expensive Fruit Stand" to buy some fruit. Bart bought 2 pomegranates and 1 kiwi for exactly $16. Lisa bought one pomegranate and 2 kiwis for exactly $11. Maggie bought 1 pomegranate …