Question

A box contains x white, y red, z blue balls. A ball is drawn at random then, what is the probability of drawing a blue ball?

Answer 1

Hint: To find the probability, we have to find the total number of balls in the box. The total number of balls is calculated irrespective of the colour of the ball. Then we will find the number of blue balls from the given information and divide it by the total number of balls. This will give us the probability of drawing a blue ball.

Complete step by step solution:
First of all, we will find the total number of balls in the box, irrespective of the colour of the ball. Following are the colours and the number of balls.
White 🡪 x balls
Red 🡪 y balls
Blue 🡪 z balls
Now, we add the balls to get the total number of balls as
white balls + red balls + blue balls = x + y + z
Therefore, the total number of balls in the box is (x + y + z) balls.
The probability of drawing a blue ball is given by the ratio of number of blue balls in the box and total number of balls in the box.
As we know, the number of blue balls in the box is z and the total number of balls in the box is (x + y + z).
Therefore, probability will be given by $\text{P}(\text{blue}\ \text{ball})=\dfrac{x}{x+y+z}$ .

Note: Probability is defined by the ratio of the number of elements of the event set to the number of elements of the sample set. The event set contains all the possible occurrences of the required event, whereas the sample set contains all the possible events.