Question

The probability I take a nap today is 4/5. The probability I will take a nap and a bubble bath today

Answer 1

Use Bayes Theorem to compute that probability. I will denote bath as $B$ and nap as $N$, the probability will be denoted as $P(B)$ or $P(N)$.

By Bayes Theorem

$P(B\mid N)=\frac{P(N\mid B)\cdot P(B)}{P(N)}$

Which reads,

"What is the probability of $B$ given $N$".

We know that $P(N\mid B)$ is 1 because we already took a bath. So the formula simplifies to,

$P(B\mid N)=\frac{P(B)}{P(N)}$

Now insert the data,

$P(B\mid N)=\frac{1/5}{4/5}=\boxed{\frac{1}{4}}$

So the probability that you will take a bath is $0.25$ after you have taken a nap.

Hope this helps. :)