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# An urn contains 9 red, 7 white, and 4 black balls.

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

Solution:

We know that,

Probability of occurrence of an event

$=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$

By permutation and combination, total no. of ways to pick r objects from given $n$ objects is ${ }^{n} C_{r}$

Now, total no.of ways to pick a ball from 20 balls is ${ }^{20} \mathrm{C} 1=20$

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 ${ }^{13} \mathrm{C}_{1}=13$

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 $\frac{13}{20}$