Question

An urn contains 9 red, 7 white, and 4 black balls. A ball is drawn at random. Find the probability that the ball is drawn is not white

Answer 1

We know that, 

Probability of occurrence of an event

 = \(\frac{Total\,no.of\,Desired\,outcomes}{Total\,no.of\,outcomes}\) 

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 = \(\frac{13}{20}\)

Conclusion: Probability of not picking a white ball from 9 red, 7 white, and 4 black balls is  \(\frac{13}{20}\)