Australian AMC 2020 - Senior Question 13

Question 13

In Paradise, all days are either fine or wet.
If today is fine, the probability of tomorrow being fine is $\frac34$.
If today is wet, the probability of tomorrow being fine is $\frac13$.
Today is Friday and it is fine. I am having a BBQ on Sunday. What is the probability that it will be fine on Sunday?

$\frac{25}{48}$
$\frac{29}{48}$
$\frac23$
$\frac34$
$\frac{31}{48}$