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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

white or black

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 ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}$

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 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 ${ }^{16} \mathrm{C}_{1}=16$

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

$=\frac{11}{20}$

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