We know that,

Probability of occurrence of an event

By permutation and combination, total no.of ways to pick r objects from given n objects is ⁿC_r

Now, total no.of ways to pick a ball from 20 balls is ²⁰c₁ = 20

Our desired output is to pick a black or red ball(not white). So, no.of ways to pick a black or red ball from 13 balls (because there are a total of 13 balls which are either red or black) is ¹³c₁ = 13

Therefore, the probability of not picking a white ball

Conclusion: Probability of not picking a white ball from 9 red, 7 white, and 4 black balls is