Question

The probability of selecting a blue marble at random from a jar that contains only black blue and green marbles is $\dfrac{1}{5}$the probability of selecting a black marble at random from the same jar is $\dfrac{1}{4}$. If the jar contains $11$ green marbles, find the total number of marbles in the jar.

Answer 1

Hint: Here we use the concept of probability.
Required formula: $P(Event){\rm{ }} = {\rm{ }}\dfrac{{favouarable{\rm{ }}cases}}{{total{\rm{ }}cases}}$
Sum of all the probabilities of events $ = 1$
Given: A jar contains only black , blue and green marbles.
$P(blue) = \dfrac{1}{5}$
$P(black) = \dfrac{1}{4}$
Number of green marbles $ = 11$

Complete step by step solution:
According to the question, $P(blue){\rm{ + }}P(black){\rm{ + }}P(green){\rm{ = 1}}$
$\dfrac{1}{5} + \dfrac{1}{4} + P(green) = 1$
$P(green) = 1 - \dfrac{1}{5} - \dfrac{1}{4}$=$\dfrac{{Number{\rm{ }}of{\rm{ }}green{\rm{ }}marbles}}{{Total{\rm{ }}marbles}} = \dfrac{{11}}{{20}}$
$\begin{array}{l}
\dfrac{{11}}{{Total{\rm{ }}marbles}} = \dfrac{{11}}{{20}}\\
\therefore Total{\rm{ }}marbles = 20
\end{array}$
Note: In these types of problems,first simplify the ratio and then equate it with the LHS. Do not equate without simplifying the ratios.