I own several cookbooks; my two favorites are “The Advanced Recipe Collection” and the “The Book of Basic Recipes”. The Advanced Recipe Collection (A) has 100 recipes that are either main dishes, starters or both. There are 60 recipes for main dishes of which 20 can also be used starters, and the remaining 40 recipes are only for starters and would not be used as main courses. The Book of Basic Recipes (B) has 150 recipes: 90 are for ‘main dishes’; the rest are for ‘starters’, none are in both categories.
I own several cookbooks; my two favorites are “The Advanced Recipe Collection” and the “The Book of Basic Recipes”.
The Advanced Recipe Collection (A) has 100 recipes that are either main dishes, starters or both. There are 60 recipes for main dishes of which 20 can also be used starters, and the remaining 40 recipes are only for starters and would not be used as main courses.
The Book of Basic Recipes (B) has 150 recipes: 90 are for ‘main dishes’; the rest are for ‘starters’, none are in both categories.
For consistency, use the following notation:
A = Pick Recipe from The Advanced Recipe Collection
B = Pick Recipe from The Basic Book of Recipes
M = Recipe is a Main Dish
S = Recipe is a Starter (i.e. a first course of a meal, also known as an appetizer)
Question: Suppose I pick one of the books at random – say, by flipping a coin -- then select a recipe at random from that book. What is P(M)?
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