Bayes' Theorem for Murfin Probability

A local bakery sells two distinct types of muffins: blueberry and chocolate. Last week, 70% of the muffins sold were blueberry, while 30% were chocolate. Due to a special promotion, if a muffin is chocolate, there is a 90% chance it was sold on the weekend, and only a 50% chance for blueberry muffins. If you randomly select a muffin that was sold on the weekend, what is the probability that it is a chocolate muffin?

To find this probability, we can use Bayes' Theorem. We denote:

- $B$: event that a muffin is blueberry.

- $C$: event that a muffin is chocolate.

- $W$: event that a muffin was sold on the weekend.

Using Bayes' Theorem, we can express the probability as:

$$P(C|W) = \frac{P(W|C) \cdot P(C)}{P(W)}$$