Question

A box contains \[50\] coloured stones. What is the total number of orange stones in the box if the probability of selecting an orange stone is \[0.4\]
(A) \[20\]
(B) \[0\]
(C) \[10\]
(D) \[40\]

Answer 1

Hint: To solve this question we must know the formula for evaluating probability of any event i.e., \[P = \dfrac{{Favourable{\text{ }}outcomes}}{{Total{\text{ }}outcomes}}\] .In the question it is given that a box contains \[50\] coloured stones and the probability of selecting an orange stone is \[0.4\] and we have to find the total number of orange stones in the box. So first, we let the total number of orange stone in the box be \[x\] ,then we find the probability of selecting an orange stone and after that equate it with the given probability to find \[x\]

Complete step-by-step answer:
It is given that a box contains \[50\] coloured stones.
So, the total outcomes for the event of selecting a stone is equals to \[50\]
i.e., Total outcomes \[ = 50\]
Now, let the number of orange stone in the box be \[x\]
So, the favourable outcome for selecting an orange stone be \[x\]
i.e., Favourable outcome \[ = x\]
Now, we will use the formula for calculating probability of selecting an orange stone
i.e., \[P = \dfrac{{Favourable{\text{ }}outcomes}}{{Total{\text{ }}outcomes}} = \dfrac{x}{{50}} - - - \left( 1 \right)\]
Now, it is given that probability of selecting an orange stone is \[0.4\]
So, equate it with the equation \[\left( 1 \right)\] we get,
\[\dfrac{x}{{50}} = 0.4\]
\[ \Rightarrow x = 0.4 \times 50\]
On multiplying, we get
\[x = 20\]
Hence, the total number of orange stone in the box is \[20\]
So, the correct answer is “Option A”.

Note: The student can make errors if they don’t have any information about the formula for calculating the probability of an event, so basic knowledge about probability is essential. And while equating, do the calculations properly to avoid mistakes. Also, when doing probability questions, always remember that the probability of an event lies between zero and one (including zero and one). i.e., \[0 \leqslant P\left( E \right) \leqslant 1\]