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# A Box Contains 10 White, 6 Red and 10 Black Balls. a Ball is Drawn at Random from the Box. What is the Probability that the Ball Drawn is Either White Or Red? - Mathematics

A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red?

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#### Solution

There are 10 + 6 + 10 = 26 balls in total.
So, the total number of possible outcomes is 26.
Consider the following events:
W = event of drawing a white ball
R = event of drawing a red ball
Then n(W) = 10 and n(R) = 6
Since both the events are mutually exclusive, we have:
(A ∩ B) = 0

$\therefore P\left( A \right) = \frac{10}{26}, P\left( B \right) = \frac{6}{26}$  and P (A ∩ B) = 0

By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
= $\frac{10}{26} + \frac{6}{26} - 0$

= $\frac{16}{26} = \frac{8}{13}$

Hence, the probability that the ball drawn is either white or red is $\frac{8}{13}$ .

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.4 | Q 17 | Page 68
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