Answer
424.8k+ views
Hint: Here we find chances of a coin being a sovereign from all three purses separately
* If there are $n$ equally likely objects then the chance of selecting one object from $n$ equally likely objects is equal to $\dfrac{1}{n}$.
* Rule of product: If there are $m$ ways to do something and $n$ to do another thing, then there are $m \times n$ ways to do both things.
* Rule of sum: if there are ${r_1}$ possible outcomes for an event and ${r_2}$ possible outcomes for another event and the two events cannot both occur, then there are ${r_1} + {r_2}$ total possible outcomes for the events.
Complete step-by-step answer:
Since each purse is equally likely to be taken, the change of selection one purse from total $3$ purses is $\dfrac{1}{3}.$
Find the chance of drawing a sovereign from the first purse.
There are $4$ ($1$ sovereign$ + 3$ Shillings) coins in first purse, hence the chance of drawing a sovereign is given by number of shillings divided by number of coins $ = \dfrac{1}{4}$
$\therefore $ Chance of drawing a sovereign from first purse is $\dfrac{1}{3} \times \dfrac{1}{4} = \dfrac{1}{{12}}$ (Using rule of product)
Find the chance of drawing a sovereign from the second purse.
There are $6$ ($2$ sovereign$ + 4$ Shillings) coins in second purse, hence the chance of drawing a sovereign is given by number of shillings divided by number of coins $ = \dfrac{2}{6}$
$\therefore $ Chance of drawing a sovereign from second purse is $\dfrac{1}{3} \times \dfrac{2}{6} = \dfrac{1}{9}$ (Using rule of product)
Find the chance of drawing a sovereign from the third purse.
There are $4$ ($3$ sovereign$ + 1$ Shillings) coins in third purse, hence the chance of drawing a sovereign is given by number of shillings divided by number of coins $ = \dfrac{3}{4}$
$\therefore $ Chance of drawing a sovereign from second purse is $\dfrac{1}{3} \times \dfrac{3}{4} = \dfrac{1}{4}$ (Using rule of product)
Find a chance of getting a sovereign, when a coin is taken out of one of the purses randomly. We calculate the sum of all chances from the first, second and third purse.
Therefore, using the rule of sum, where each event of taking out a sovereign from each purse is an independent event.
$\therefore $ Chance of coin to be a sovereign \[ = \dfrac{1}{{12}} + \dfrac{1}{9} + \dfrac{1}{4}\]
By taking LCM on the RHS of the equation.
\[
= \dfrac{{3 + 4 + 9}}{{36}} \\
= \dfrac{{16}}{{36}} \\
= \dfrac{4}{9} \\
\]
Thus, the chance of a coin to be a sovereign is \[\dfrac{4}{9}\].
Note: Students are likely to make mistakes applying combination or permutation formulas to this question which is wrong because here we don’t have to find a number of ways in which we can pick a sovereign, we have to find a chance or in other words probability.
* If there are $n$ equally likely objects then the chance of selecting one object from $n$ equally likely objects is equal to $\dfrac{1}{n}$.
* Rule of product: If there are $m$ ways to do something and $n$ to do another thing, then there are $m \times n$ ways to do both things.
* Rule of sum: if there are ${r_1}$ possible outcomes for an event and ${r_2}$ possible outcomes for another event and the two events cannot both occur, then there are ${r_1} + {r_2}$ total possible outcomes for the events.
Complete step-by-step answer:
Since each purse is equally likely to be taken, the change of selection one purse from total $3$ purses is $\dfrac{1}{3}.$
Find the chance of drawing a sovereign from the first purse.
There are $4$ ($1$ sovereign$ + 3$ Shillings) coins in first purse, hence the chance of drawing a sovereign is given by number of shillings divided by number of coins $ = \dfrac{1}{4}$
$\therefore $ Chance of drawing a sovereign from first purse is $\dfrac{1}{3} \times \dfrac{1}{4} = \dfrac{1}{{12}}$ (Using rule of product)
Find the chance of drawing a sovereign from the second purse.
There are $6$ ($2$ sovereign$ + 4$ Shillings) coins in second purse, hence the chance of drawing a sovereign is given by number of shillings divided by number of coins $ = \dfrac{2}{6}$
$\therefore $ Chance of drawing a sovereign from second purse is $\dfrac{1}{3} \times \dfrac{2}{6} = \dfrac{1}{9}$ (Using rule of product)
Find the chance of drawing a sovereign from the third purse.
There are $4$ ($3$ sovereign$ + 1$ Shillings) coins in third purse, hence the chance of drawing a sovereign is given by number of shillings divided by number of coins $ = \dfrac{3}{4}$
$\therefore $ Chance of drawing a sovereign from second purse is $\dfrac{1}{3} \times \dfrac{3}{4} = \dfrac{1}{4}$ (Using rule of product)
Find a chance of getting a sovereign, when a coin is taken out of one of the purses randomly. We calculate the sum of all chances from the first, second and third purse.
Therefore, using the rule of sum, where each event of taking out a sovereign from each purse is an independent event.
$\therefore $ Chance of coin to be a sovereign \[ = \dfrac{1}{{12}} + \dfrac{1}{9} + \dfrac{1}{4}\]
By taking LCM on the RHS of the equation.
\[
= \dfrac{{3 + 4 + 9}}{{36}} \\
= \dfrac{{16}}{{36}} \\
= \dfrac{4}{9} \\
\]
Thus, the chance of a coin to be a sovereign is \[\dfrac{4}{9}\].
Note: Students are likely to make mistakes applying combination or permutation formulas to this question which is wrong because here we don’t have to find a number of ways in which we can pick a sovereign, we have to find a chance or in other words probability.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)