Books of Calvin
Calvin was Solve Problems in Brilliant, When forgot What Theorem That he should wear on a Question, Calvin decided Search the Book that contained the theorem that he forgot , He was on search of Book In A Bookcase that contained 20 Books, Being 12 Mathematics and Physics 8. Later he removed 2 Books and Without Replacement. What is the probability he Retrieved 2 Books of Math ?
Note : can be written as where and are coprime positive integers.
Find
The answer is 128.
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1 solution
It's evident that there is a 12/20 chance of picking the first Math book. Once the first Math book is chosen (and not replaced) the sample space changes (19 books remain) and you can only chose from the remaining 11 Math books. Hence, there is a 11/19 chance of picking the second Math book.
On both occasions when we have to pick a book, we must realise that they are independent events. As a result, we must multiply the individual probabilities together the get out final answer.
12/20 x 11/19 = 33/95
From here we see that a = 33 and b = 95, thus a + b = 128