Question

A jar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is \[\dfrac{1}{3}\], and the probability of selecting a green marble at random is \[\dfrac{4}{9}\]How many white marbles does the jar contain ?

Answer 1

Hint: To solve this question we will first of all calculate the number of blue marble and the number of green marbles using the probability given of both the marbles. Then we will use this fact that the sum of all the three numbers of marbles is 54, to get the value of the number of white marbles.
Complete step-by-step answer:
Given that a jar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is \[\dfrac{1}{3}\], and the probability of selecting a green marble at random is \[\dfrac{4}{9}\].
We have to find the number of white marbles in the jar.
We will first of all find the number blue and green Marbles.
It is given that the total number of Marbles are (including blue, green, white) = 54
Probability of selecting a blue ball is given to be = \[\dfrac{1}{3}\]
Let the number of blue marbles be b then we have,
\[\begin{align}
  & \dfrac{1}{3}=\dfrac{b}{54} \\
 & \Rightarrow b=\dfrac{54}{3} \\
 & \Rightarrow b=18 \\
\end{align}\]
Therefore, the number of blue Marbles is = 18.
Similarly, we will proceed to calculate the number of green marbles.
Probability of selecting green marble = \[\dfrac{4}{9}\]
Let the number of green marbles be g then we have,
\[\begin{align}
  & \dfrac{4}{9}=\dfrac{g}{54} \\
 & \Rightarrow g=\dfrac{54(4)}{9} \\
 & \Rightarrow g=24 \\
\end{align}\]
Therefore, the number of green marbles is = 24 marbles.
Now let the number of White marbles be x,
Now it is given that,
Blue + green + white = 54.
Therefore, substituting the values obtained of blue and green marbles in above we get,
\[\begin{array}{*{35}{l}}
   \Rightarrow 18\text{ }+\text{ }24\text{ }+\text{ }x\text{ }=\text{ }54 \\
   \Rightarrow 42\text{ }+\text{ }x\text{ }=\text{ }54 \\
   \begin{align}
  & ~\Rightarrow x\text{ }=\text{ }54\text{ }-\text{ 42} \\
 & \Rightarrow x\text{ }=12 \\
\end{align} \\
\end{array}\]
So, the number of white marbles is 12.

Note: The possibility of error in this type of question can be directly calculating the probability of the white marble and not going for calculating the number of it, which will lead to calculation mistakes and therefore wrong result. Always go for calculating the number of blue and green marble first then proceed for any further calculation.