Question

A bag contains 20 silver balls and x iron balls. If one ball is drawn from the bag, what is the probability that it is iron.

Answer 1

Hint: In this question, we need to check the number of possible outcomes for the ball drawn from the bag to be iron and find the total number of outcomes possible. Then using the probability formula which is given by \[P=\dfrac{m}{n}\] which on further simplification gives the result of the drawn ball to be iron.

Complete step by step answer:
PROBABILITY: If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A, denoted by P(A), is given by
\[P\left( A \right)=\dfrac{m}{n}=\dfrac{\text{number of favourable outcomes}}{\text{total number of possible outcomes}}\]
Now, from the given conditions in the question we have 20 silver balls and x iron balls
Here, the number of favourable outcomes for the ball to be iron is given by
\[m=x\]
Let us now find the total number of possible outcomes which is given by
\[n=20+x\]
Now, the probability for the ball to be drawn at random not red is given by
\[\Rightarrow P=\dfrac{m}{n}\]
Now, on further substituting the respective values we get,

\[\therefore P=\dfrac{x}{20+x}\]

Note: Instead of finding the probability for the ball drawn at random to be iron we can also solve this by finding the probability for the ball drawn to be silver and then subtracting if from 1 which also gives the same result as these events are complement to each other.
\[\begin{align}
  & \Rightarrow 1-\dfrac{20}{20+x} \\
 & \Rightarrow \dfrac{x}{20+x} \\
\end{align}\]
It is important to note that while calculating the probability there is a chance to directly write the probability as choosing one ball out of x but here in the bag there are 20 silver and x iron balls out of which we need to choose 1 iron ball.