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?

Answer 1

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 $\frac{8}{13}$.