Question

A bag contains \[54\]balls, each of them is either red, grey, and pink. The probability of selecting a red ball from the bag is $\dfrac{1}{3}$ and that of selecting a grey ball is $\dfrac{4}{9}$ . Then, the number of pink balls are
1.\[10\]
2.\[18\]
3.\[12\]
4.\[24\]

Answer 1

Hint: To deal with the problem, we simply need to find the probability of selecting the pink ball. Then, we can find out the number of pink balls using the total number of balls.


Complete step by step solution:
We are given that: A bag contains \[54\]balls, some are red, grey and pink
Probability of selecting a red ball from bag \[ = \dfrac{1}{3}\]
Probability of selecting a grey ball from bag \[ = \dfrac{4}{9}\]
We need to find no. of pink ball
We will calculate probability of pink ball
So, Total probability of all balls \[ = {\text{ }}1\]
\[P\left( {grey} \right){\text{ }} + {\text{ }}p\left( {red} \right){\text{ }} + p\left( {pink} \right){\text{ }} = {\text{ }}1\]
\[\dfrac{4}{9} + \dfrac{1}{3} + x = 1\]
$x = \dfrac{2}{9}$
\[So,{\text{ }}p\left( {Pink} \right){\text{ }} = \dfrac{{PinkBalls}}{{TotalBalls}}\]
\[ = \dfrac{2}{9} = \dfrac{x}{{54}}\]
\[ = \dfrac{2}{9} \times 54 = x\]
\[\;x = 12\]
∴The Pink Balls In the bag are 12


Note: Students should remember that total probability is equal to one.
Also, to find no. of pink balls, we compared the probability of pink balls with the probability of pink balls using the actual number of balls given.So find the probability in accordance to the unknown data which has to be found out