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.  Find the probability that the cake got a "thumbs up".

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. 
 
Find the probability that the cake got a "thumbs up".

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