Help with bayes theorem problem

Please help! This one is so confusing for me! Show work if possible

A local TV station employs Desmorelda, "Mistress of the Zodiac", as its weather forecaster. Now, when it rains, Sagittarius is in the shadow of Jupiter one-third of the time, and it rains on 2 out of every 45 days. Sagittarius falls in Jupiter's shadow on only 1 in every 5 rainless days. The powers that be at the station notice a disturbing pattern to Desmorelda's weather predictions. It seems that she always predicts that it will rain when Sagittarius is in the shadow of Jupiter. What percentage of the time is she correct? (Round your answer to the nearest whole percent.)

For a given day, let's first define events and gather the given information.
Let R = event that it rains that day, and S = the event that Sagittarius is in Jupiter's shadow that day.
We are given the following information:

P(S given R) = 1/3; P(R) = 2/45; P(S given not R) = 1/5.

We need to find P(R given S).

P(R given S) = P(R and S)/P(S)
= P(R and S)/[P(R and S) + P((not R) and S)]
= P(R)P(S given R) / [P(R)P(S given R) + P(not R)P(S given not R)]
= (2/45)(1/3) / [(2/45)(1/3) + (43/45)(1/5)]
= (2/135)/(2/135 + 43/225)
= (10/675)/(10/675 + 129/675)
= 10/(10 + 129)
= 10/139 or about 7%.

She is correct only about 7% of the time.

Lord bless you today!