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 red

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 red ball. So, no. of ways to pick a red ball from 9 red balls (because the red ball can be picked from only red balls) is ⁹c₁ = 9

Therefore, the probability of picking a red ball = \(\frac{9}{20}\)

Conclusion: Probability of picking a red ball from 9 red, 

7 white and 4 black balls is  \(\frac{9}{20}\)