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 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 white ball. So, no. of ways to pick a white ball from 7 white balls(because the white ball can be picked from only white balls) is ⁷c₁ = 7 

Therefore, the probability of picking a white ball = \(\frac{7}{20}\)

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

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