Question

A purse contains \[10\] five hundred rupee notes, \[20\] hundred rupee notes, \[30\] fifty rupee notes and \[40\] ten rupee notes. If it is likely that one of the notes will fall out when the purse turns upside. What is the probability that the note will not be a five hundred rupee note?
(A). $ \dfrac{7}{{10}} $
(B). $ \dfrac{9}{{10}} $
(C). $ \dfrac{3}{{10}} $
(D). None of these

Answer 1

Hint: We should know the formulas of simple probability of an event which can be given as Probability of an event $ P\left( E \right) $ $ = \dfrac{{Number\;of\;successful\;outcomes}}{{Total\;number\;of\;possible\;outcomes\;}} $
Also, we should know the formula of Probability of not an event $ P(E)' $ $ = 1 - P(E) $

Complete step-by-step answer:
Given in the question,
Number of five hundred rupees note \[ = 10\]
Number of hundred rupees note \[ = 20\]
Number of fifty rupees note \[ = 30\]
Number of ten rupees note \[ = 40\]
Total number of notes in the purse \[ = 10 + 20 + 30 + 40 = 100\]
As we know probability of an event $ P\left( E \right) $ $ = \dfrac{{Number\;of\;successful\;outcomes}}{{Total\;number\;of\;possible\;outcomes\;}} $
And, Probability of not an event $ P(E)' $ $ = 1 - P(E) $ \[\]
Here, Probability of the note which fell to be a five hundred rupee note $ = \dfrac{{10}}{{100}} $ $ = \dfrac{1}{{10}} $
So, the probability of the note which fell not to be a five hundred rupee note
 $ = 1 - \dfrac{1}{{10}} = \dfrac{{10 - 1}}{{10}} = \dfrac{9}{{10}} $
Therefore, the probability that the note will not be a five hundred rupee note is \[\left( b \right)\] $ \dfrac{9}{{10}} $ .
So, the correct answer is “Option B”.

Note: Probability of an event \[E{\text{ }} + \] Probability of the event not \[E{\text{ }} = {\text{ }}1\] . Also, we should know about the definition of probability and formula of probability of happening an event to solve these types of problems.