Question

A purse contains 10 five hundred rupee note, 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: The probability of an event is equal to the ratio of number of possible outcomes to the total number of outcomes. Let E be the event occurred, then the probability of event E is given by P(E), and the formula is given by,
\[P\left( E \right) = \dfrac{{{\text{Number of favourables outcomes to E}}}}{{{\text{Total number of outcomes}}}}\],
Probability of event not occurring is denoted by\[P\left( {\overline E } \right)\], and probability of even occurring and probability of event not occurring will always be equal to 1, I,e.,\[P\left( E \right) + P\left( {\overline E } \right) = 1\].

Complete step-by-step answer:
Given that a purse contains 10 five hundred rupee note, 20 hundred rupee notes, 30 fifty rupee notes and 40 ten rupee notes,
From the given data,
Number of five hundred rupee notes= 10,
Number of hundred rupee notes=20,
Number of fifty rupee notes=30,
Number of ten rupee notes=40.
Total number of notes = 10+20+30+40 = 100.
Let E be the event of the note will not be a five hundred rupee note,
Now here number of possible outcomes that the note will be a five hundred rupee note =10,
Total number of outcomes = 100,
Using probability formula we get,
\[P\left( E \right) = \dfrac{{{\text{Number of favourables outcomes to E}}}}{{{\text{Total number of outcomes}}}}\],
Substituting the values we get,
\[P\left( E \right) = \dfrac{{10}}{{100}} = \dfrac{1}{{10}}\],
So the probability that the note that would fall is a five hundred rupee note=\[\dfrac{1}{{10}}\],
We have to find the probability that the note is not a five hundred rupee note, i.e,\[P\left( {\overline E } \right)\],
Using the formula, \[P\left( E \right) + P\left( {\overline E } \right) = 1\],
Here \[P\left( E \right) = \dfrac{1}{{10}}\], now substituting the values we get,
\[\dfrac{1}{{10}} + P\left( {\overline E } \right) = 1\],
\[ \Rightarrow P\left( {\overline E } \right) = 1 - \dfrac{1}{{10}}\]
\[ \Rightarrow P\left( {\overline E } \right) = \dfrac{9}{{10}}\],
The probability that the note is not a five hundred rupee note is\[\dfrac{9}{{10}}\],

\[\therefore \] The probability that the note is not a five hundred rupee note is\[\dfrac{9}{{10}}\], so from the options, option B is correct.

Note:
Students should know the definition and formulas related to probability in solving these types of questions and students should read the question correctly, and should apply the probability formula with the correct values, as there is a chance of making mistakes in getting the values correctly.