Question

In Spetember of 2013, Mario The Baker introduced a new chocolate cake and hired Doug and Jeremy to bake these cakes. Every customer buying this new chocolate cake either gives it a "thumbs up" or a "thumbs down". Based on the data accumulated between 10/2013 and 9/2014, we know that 40% of the cakes baked by Doug gets a "thumbs up", while only 10% of those baked by Jeremy gets a "thumbs up". About 70% of the cakes are baked by Doug. One cake was selected at random on 10/01/2014 and got a "thumbs up".

1. Find the probability that the cake was baked by Doug.

Answer 1

There is a 90.32% probability that the cake was baked by Doug.

Explanation:

We have these following probabilities:

A 70% probability that Doug bakes the cake.

A 30% probability that Jeremy bakes the cake.

A 40% probability that a cake baked by Doug gets a thumbs up.

A 10% that a cake baked by Jeremy gets a thumbs up.

One cake was selected at random on 10/01/2014 and got a "thumbs up".

1. Find the probability that the cake was baked by Doug.

The probability that a baked cake gets a thumbs up is:

`P = 0.7*0.4 + 0.3*0.10 = 0.31`

Of those, 0.7*0.4 = 0.28 are baked by Doug.

So the probability is:

`P = (0.28)/(0.31) = 0.9032`

There is a 90.32% probability that the cake was baked by Doug.