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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 red

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 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 ${ }^{9} \mathrm{C}_{1}=9$

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 $\frac{9}{20}$

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