# Tories bookcase holds one algebra book one geometry book and 12 books about advanced engineering mathematics. Books are taken at random from her book case, one after another without replacement until an engineer book is had, at which no more books are taken. The random variable Z represents the total number of books taken during this experiment. Find Pr[z=3]

Question
Upper Level Math
Tories bookcase holds one algebra book one geometry book and 12 books about advanced engineering mathematics. Books are taken at random from her book case, one after another without replacement until an engineer book is had, at which no more books are taken. The random variable Z represents the total number of books taken during this experiment.
Find $$\displaystyle{P}{r}{\left[{z}={3}\right]}$$

2021-02-09
Step 1
Given information
Torries bookcase holds
1 algebra book
1 geometry book
Total books = 14
Books are taken until engineering book has been taken
Let z denotes the total number of books taken
Step 2
Z=3 means the first two must be other than engineering books and last must be the engineering book
$$\displaystyle{P}{\left({Z}={3}\right)}=\frac{{2}}{{14}}\times\frac{{1}}{{13}}\times\frac{{12}}{{12}}=\frac{{1}}{{91}}={0.011}$$(Rounded upto 3 decimals places)

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