Question

A purse contains a number of $Rs.1,Rs.2$ and $Rs.5$ coins as given below

RS. 1	RS.2	RS.5
10	14	14

If from the purse a coin is taken at random, then find the probability that the coin
(i) is not a $Rs.1$coin.
(ii) is a $Rs.3$coin ?

Answer 1

Hint:In this question ,we will use the concept of probability of event ‘not A’ . Then according to the given details in the question we will find the answer. We will use the method of finding of probability of event ‘not A’ i.e. $P(notA) = 1 - P(A)$.First find probability of getting Rs 3 coin from the purse and next subtract it from 1 to get required probability i.e. probability of not getting Rs 3 coin from the purse.For determining probability favourable outcomes i.e chances of getting outcomes while doing random experiment should have some value,if there is no favourable outcome then probability is 0.

Complete step-by-step answer:
Here we have , $10{\text{ }}Rs.1$coin ,$14{\text{ }}Rs.2$coin and $14{\text{ }}Rs.5$ coin.
$\Rightarrow$ total number of coins = $38$ coins.
(i). Given that , number of $Rs.1$coin = $10{\text{ }}$
A coin is taken at random from the purse and we have to find the probability that the drawn coin is not a $Rs.1$ coin.
We know that, $P(notA) = 1 - P(A)$
So, probability that the drawn coin is $Rs.1$ coin
$\Rightarrow P(Rs.1{\text{ coin) = }}\dfrac{{{\text{number of }}Rs.1{\text{ coin}}}}{{{\text{number of total coins in the purse }}}} \\\ \\\ \Rightarrow P(Rs.1{\text{ coin) = }}\dfrac{{10}}{{10 + 14 + 14}} = \dfrac{{10}}{{38}} \\\$
Hence, probability that the drawn coin is not a $Rs.1$ coin
$\Rightarrow P(not{\text{ }}Rs.1{\text{ coin) = 1 - }}P(Rs.1{\text{ coin)}} \\\ \Rightarrow P(not{\text{ }}Rs.1{\text{ coin) = 1 - }}\dfrac{{10}}{{38}} = \dfrac{{38 - 10}}{{38}} = \dfrac{{28}}{{38}} \\\ \Rightarrow P(not{\text{ }}Rs.1{\text{ coin) = }}\dfrac{{14}}{{19}} \\\$

(ii). Here ,we have number of $Rs.3$ coin = 0
So, the probability that the drawn coin is a $Rs.3$ coin
$\Rightarrow P(Rs.3{\text{ coin) = }}\dfrac{{{\text{number of }}Rs.3{\text{ coin}}}}{{{\text{number of total coins in the purse }}}} \\\ \\\ \Rightarrow P(Rs.3{\text{ coin) = }}\dfrac{0}{{10 + 14 + 14}} = 0 \\\$
Hence, $P(Rs.3{\text{ coin) = 0}}$

Note: In this type of question, first we have to know what we have to find. Here, we have number of coins and we have to find the probability on some cases by using the formula of probability i.e. $\Rightarrow {\text{ }}\dfrac{{{\text{favourable outcomes}}}}{{{\text{total number of outcomes}}}}$.
Through this we will get the required answer.