Question

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag.

Answer 1

- Hint: For solving this problem, let the number of blue balls be x. Now the total number of balls in the bag are (5 + x). By using the given condition that the probability of drawing a blue wall is double the probability of drawing a red ball, we form an equation in terms of x. By solving this equation, we easily evaluated the number of blue balls.

Complete step-by-step solution -

The total number of red balls = 5.
Let, the total number of blue balls be ‘x’.
Formula of probability is:
P(Event) $=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
Now, using the above formula, the probability of getting red ball from the bag is:
P (Getting a red ball) $=\dfrac{\text{Total number of red balls}}{\text{Total number of balls in the bag}}$
Total number of balls in the bag = number of red balls + number of blue balls
Total number of balls in the bag = 5 + x.
P (Getting a red ball) $=\dfrac{5}{x+5}$.
Similarly, the probability of getting a blue ball from the bag is:
P (Getting a blue ball) $=\dfrac{\text{Total number of blue balls}}{\text{Total number of balls in the bag}}$
Total number of balls in the bag = 5 + x.
P (Getting a blue ball) $=\dfrac{x}{x+5}$.
If the probability of drawing a blue ball is double that of red ball, using this condition the equation is:
$\begin{aligned} & \dfrac{x}{x+5}=2\times \dfrac{5}{x+5} \\\ & \Rightarrow x=2\times 5 \\\ & \Rightarrow x=10 \\\ \end{aligned}$
Hence, the total number of blue balls in the bag are 10.

Note: The key step is the assumption of blue balls to be x. We can also verify our answer from the given conditions, since the probability of blue ball is only greater if red balls are less than blues. Knowledge of probability of occurrence of an event is necessary.