Question 1001678
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.