in camelot it never rains on friday, saturday, sunday or monday. the probability that it rains on a given tuesday is $\displaystyle (1/5)$. for each of the two remaining days, wednesday and thursday, the conditional probability that it rains, given that it rained on the previous day is a, and the conditional probability that it rains, given that it did not rain on the previous day is b.

the answer for the first part of the questions is

p(raining on wednesday)=1/5(a+4b)

p(raining on thursday)=1/5(a-b)(a+4b)+b

b) if X is the event that, in a randomly chosen week, it rains on thursday, Y is the event that it rains on tuesday and y' is the event it does not rain on tuesday, show that

$\displaystyle p(x|y)-p(x|y ')=(a-b)^2$

what i did for question b was:

p(x|y)-p(x|y)

$\displaystyle =p(x \cap y)/p(y) - p(x \cap y')/p(y')$

but what i did was wrong... so help please