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

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 white or red ball. So, no. of ways to pick a white or red ball from 16 balls(because there are a total of 16 balls which are either red or white) is ¹⁶c₁ = 16 

Therefore, the probability of picking a white or black ball = \(\frac{11}{20}\) 

Conclusion: Probability of picking a white or black ball from 9 red, 7 white, and 4 black balls is  \(\frac{11}{20}\)