QUESTION

# A bank ATM has notes of denomination 100, 500 and 1000 in equal numbers. What is the probability of getting a note of Rs.1000?

Hint: To proceed these types of questions we first assume a value X which will be equal to the number of notes of 100, 500 and 1000 in the bank ATM. Now use the formula of probability which is given as probability of the event is equal to number of favourable outcomes divided by the total number of outcomes.

Given that the bank ATM has notes of denomination 100, 500 and 1000 in equal numbers. We have to find the probability of getting a note of Rs. 1000.

We have all the notes of 100, 500 and 1000 equal in number. Let the number be X.
Therefore, we have the number of notes of 100, 500 and 1000 equal to X.
Because the number of notes of 100, 500 and 1000 are equal in number therefore, adding the number of notes of 100, 500 and 1000 gives the total number of notes in the bank ATM.

Total notes in the ATM = Number of notes of 100 + Number of notes of 500 + Number of notes of 1000
$\Rightarrow X+X+X\text{ }=\text{ }3X.$

Therefore, the total number of notes in the bank ATM is 3X.

We have the formula of probability which is given as probability of the event is equal to number of favourable outcomes divided by the total number of outcomes.
Because the number of notes of 1000 is equal to X, therefore the probability of getting a 1000 note is equal to the number of notes of 1000 divided by the total number of notes in the ATM.

Applying above we get,
The probability of getting a note of $Rs.1000=\dfrac{X}{3X}$
$\Rightarrow$ The probability of getting a note of $Rs.1000=\dfrac{1}{3}$.
Hence, we obtain our result as,

The probability of getting a note of $Rs.1000=\dfrac{1}{3}$.

Note: The possibility of error in the question can arise at a point where you are assuming the number of notes as X, if you go for assuming 3 different values to the 3 different notes of 100, 500 and 1000 it will give incorrect solution, because given in the question is that all notes are equal in number.