Question

A jar contains blue and green marbles. The number of green marbles is 5 more than twice the number of blue marbles. If the probability of drawing a blue one at random is\[\dfrac{2}{7}\], how many blue and green marbles are there in a jar.

Answer 1

Hint:
Probability of any event is given as \[P\left( E \right) = \dfrac{{Number{\text{ }}of{\text{ }}favourable{\text{ }}outcomes}}{{\;Total{\text{ }}number{\text{ }}of\;outcomes}}\].
Where sample space is the set of all outcomes of the experiment.

Complete step by step solution:
Let the number of green marbles be x.
As per question, the number of blue marbles will be \[2x + 5\].
Given probability of drawing a blue one at random=\[\dfrac{2}{7}\]
Let P(B) be the probability of drawing a blue marble.
\[
   \Rightarrow P(B) = \dfrac{x}{{3x + 5}} = \dfrac{2}{7} \\
   \Rightarrow 7x = 2(3x + 5) \\
   \Rightarrow 7x = 6x + 10 \\
   \Rightarrow x = 10 \\
\]
The required number of Green marbles is 10 and that of Blue marbles is \[2(10) + 5 = 25\]

Note:
The value of probability will lie between 0 to 1 including both. If the probability of an event is 0, it will be considered as an impossible event whereas if the probability of an event is 1, it will be considered as a sure event.