Question

A bag contains a number of marbles of which 80 are red, 24 are white and the rest are blue. If the probability of randomly selecting a blue marble from this bag is $\dfrac{1}{5}$​, how many blue marbles are there in the bag?
A .25
B. 26
C. 27
D. 28

Answer 1

Hint: It is a simple but fundamental question of the probability. We can assume the number of blue balls in the bag, Further using the basic definition of the probability that number of blue balls can be easily calculated.

Complete step-by-step answer:
Data given in the question are:
Number of red balls = 80
Number of white balls = 24
Number of blue balls we will assume x.
Total balls = 80 + 24 + x
For finding the probability we need to find favourable count and total count t of the events.
Here favourable counts for getting blue ball will be = x
And total count for getting a ball from the bag = 80 + 24 + x
Now,
$probability\;of\;getting\;blue\;ball = \dfrac{{\;favourable\;for\;blue\;ball}}{{total\;count\;for\;getting\,a\,ball}}$
We will substitute the values in above formula, to get
$probability\;of\;getting\;blue\;ball = \dfrac{{\;x}}{{80 + 24 + x}}$
As given in the question the probability for getting a blue ball from the bag = $\dfrac{1}{5}$
Thus, $
  \dfrac{1}{5} = \dfrac{{\;x}}{{80 + 24 + x}} \\
   \Rightarrow \dfrac{1}{5} = \dfrac{{\;x}}{{104 + x}} \\
   \Rightarrow 5x = 104 + x \\
    \\
 $
Solving above equation we get,
x= 26
$\therefore $ There are 26 blue balls in the bag.

So, the correct answer is “Option B”.

Note: Probability is a branch of mathematics to deal and calculate the possibility of occurrence of a given event. It is expressed as a number between 1 and 0. Any event with a probability value 1 is considered as a sure event. On the other hand, any event with a probability value 0 is considered as an impossible event. In the simple form, it can be represented mathematically as the number of occurrences of some favourable event divided by the sum total of the favourable and unfavourable occurrences of the events.