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?
$
  (a){\text{ }}\dfrac{7}{{13}} \\
  (b){\text{ }}\dfrac{7}{{12}} \\
  (c){\text{ }}\dfrac{8}{{13}} \\
  (d){\text{ }}\dfrac{9}{{15}} \\
 $

Answer 1

Hint: In this question there are some balls of different colors, and a ball is to be drawn. The probability that the ball is either red or white means that we have to find the probability of union of these two events, that is we can select either red or we can select white.

Complete step-by-step answer:

Given data
In a box white balls = 10,
Red balls = 6,
Black balls = 10.

So the total balls in the box are (10 + 6 + 10) = 26 balls.

Now we have to find the probability that the ball drawn is either white or red.

As we know that the probability is the ratio of the number of favorable outcomes to the total outcomes.

So first find out the probability (Pw) that the ball drawn is white.
$ \Rightarrow {P_w} = \dfrac{{{\text{Favorable balls}}}}{{{\text{Total balls}}}} = \dfrac{{10}}{{26}}$

Now find out the probability (Pr) that the ball drawn is red.
$ \Rightarrow {P_r} = \dfrac{{{\text{Favorable balls}}}}{{{\text{Total balls}}}} = \dfrac{6}{{26}}$
So the probability (P) that the ball drawn is either white or red is
$ \Rightarrow P = {P_w} + {P_r}$

Now substitute the values in the given equation we have,
$ \Rightarrow P = \dfrac{{10}}{{26}} + \dfrac{6}{{26}} = \dfrac{{16}}{{26}} = \dfrac{8}{{13}}$
So this is the required probability that the ball drawn is either white or red.

Hence option (C) is correct.

Note: Whenever we face such types of problems the key concept is simply to have the basic understanding of the direct formula of probability which states that probability of any event is favorable outcome divided by total outcome. This concept will help to get on the right track to reach the answer.