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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,

\[\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.