Question

The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is 0.25. The probability of selecting a white marble at random from the same jar is $\dfrac{1}{3}$ . If the jar contains 10 yellow marbles. What is the total number of marbles in the jar?

Answer 1

Hint: Use the probability of occurrence of green & white marbles to find the number of green & white marbles & hence find total number of marbles.

Let us suppose a jar which contains green, white and yellow marbles only.
Given, Probability of selecting a green marble from the jar = 0.25
Probability of selecting a while marble from the jar = $\dfrac{1}{3}$
Also, given that there are 10 yellow marbles in the jar.
Let the number of green marbles and white marbles in the jar be x and y respectively.
Therefore, Total number of marbles in the jar = $x + y + 10$
As we know that the general formula for probability is given as
${\text{Probability of occurrence of an event}} = \dfrac{{{\text{Number of favourable outcomes }}}}{{{\text{Total number of outcomes}}}}$
Therefore, $\begin{gathered}
  {\text{Probability of selecting a green marble from the jar}} = \dfrac{{{\text{Number of green marbles}}}}{{{\text{Total number of marbles in the jar}}}} \\
   \Rightarrow 0.25 = \dfrac{x}{{x + y + 10}} \Rightarrow x + y + 10 = \dfrac{x}{{0.25}} = 4x \Rightarrow y + 10 = 3x \Rightarrow y = 3x - 10{\text{ }} \to {\text{(1)}} \\
\end{gathered} $
Also,
Now using equation (1) substitute the value of y obtained in the equation (2), we get

Put the value of x in equation (1), we have
$ \Rightarrow y = 3 \times 6 - 10 = 18 - 10 = 8$
Therefore, the number of green marbles and yellow marbles in the jar are 6 and 8 respectively.
Total number of marbles in the jar = x + y + 10 = 6 + 8 + 10 = 24

Note- Here, if we observe carefully in the event of selecting a green marble, the favourable case is occurrence of green marble from the jar when a marble is randomly selected and in the event of selecting a white marble, the favourable case is occurrence of white marble from the jar when a marble is randomly selected.