In the Mindworkzz library, there are $8$ books by Stephen
Covey and $1$ book by Vinay Singh in shelf $A$. At the same
time, there are $5$ books by Stephen in shelf $B$. One book
is moved from shelf $A$ to $B$. A student picks up a book
from shelf $B$. What is the probability that the book by
Vinay Singh is in shelf $B$.
$a.)\ \dfrac{3}{54} \\
b.)\ \dfrac{4}{54} \\
\color{green}{c.)\ \dfrac{5}{54} }\\
d.)\ \text{none of these} $
I did $P(\text{Singh's Book in A}) \times P(\text{Singh's Book in B})
= \dfrac{1}{9} \times \dfrac{1}{6}=\dfrac{1}{54}$
I look for a short and simple way.
I have studied maths upto $12$th grade.
Best Answer
For the desired event to happen, the book by Singh must be moved from shelf $A$ to shelf $B$, and not picked from shelf $B$, thus $Pr = \dfrac19\times\dfrac56 = \dfrac 5{54}$