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Question
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?
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
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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