You recently took up baking to try and make it to the show "Nailed it!". You have

decided to bake a cake. You have 10 bottles of powdered ingredients to use in your

cake. 2 of them contain baking soda, 3 contain corn starch, and 5 contain powdered

sugar. You are going to keep baking cakes till you bake a successful one. To bake a

cake successfully you have to use a spoon of the baking soda.

Each time you attempt to make a cake, you mix all the

rest

of the ingredients (

none of

which have baking soda

) and then randomly pick a bottle from the 10 and use a spoon

of the powder in the bottle. If it was the baking soda bottle, your cake will turn out

successful and you are done! If not, you need to start all over again and bake another

and another etc till you have a proper cake.

Any attempt using baking soda takes you 1 hour and 30 minutes to mix and bake.

Any attempt using corn starch takes you 1 hour and 15 minutes to mix and bake.

Any attempt with powdered sugar takes you 2 hours to mix and bake.

What is the expected amount of time it will take you to successfully bake a cake?

(Assume that you don't rest between discovering a flopped cake and restarting baking

the next cake.)