SOLUTION: Alexis often gets her clothes dirty during meals because she's a messy eater especially eating pasta. Her mother cooks pasta twice a week. so if Alexis has pasta. her clothing is d

Algebra ->  Probability-and-statistics -> SOLUTION: Alexis often gets her clothes dirty during meals because she's a messy eater especially eating pasta. Her mother cooks pasta twice a week. so if Alexis has pasta. her clothing is d      Log On


   



Question 1001678: Alexis often gets her clothes dirty during meals because she's a messy eater especially eating pasta. Her mother cooks pasta twice a week. so if Alexis has pasta. her clothing is dirty 1 out of 2 times. Days Alexis does not have pasta, her clothes are clean 2 out of 3. what is the probability she would have a clean dress today
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
clean means her clothes are clean.
dirty means her clothes are dirty.
pasta means she ate pasta.
no pasta means she didn't eat pasta.

you are given that her mother cooks pasta for her 2 times a week.

therefore:

p(pasta) = 2/7
p(no pasta) = 5/7

you are given that her clothes are dirty 1 out of 2 times that she eats pasta.

this means that her clothese are clean 1 out of 2 times that she eats pasta.

therefore:

p(clean given pasta) = 1/2

you are given that her clothes are clean 2 out of 3 times that she doesn't eat pasta.

therefore:

p(clean given no pasta) = 2/3

you want to know the probability that she'll have a clean dress today.

the probability that she'll have a clean dress today = p(pasta) * p(clean given pasta) + p(no pasta) * p(clean given no pasta).

that formula becomes:

the probability that she'll have a clean dress today = (2/7 * 1/2) + (5/7 * 2/3).

2/7 * 1/2 = 2/14 = 1/7

5/7 * 2/3 = 10/21

1/7 + 10/21 = 3/21 + 10/21 = 13/21.

the probability that she'll have a clean dress today is 13/21.