Question

box contains 18 balls out of which 'x' are blue and others are red in colour. The number of red balls is half the number of blue balls. what is the probability that a ball drawn at random is a blue ball? what is the probability that a ball drawn at random is a red

Answer 1

Answer:

let no of balls blue is x so red are 1/2x

total balls x+1/2x

=3x/2

p(E) of blue balls=x/3x/2=2/3

red balls=1/2x/3x/2

=1/3

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The probabilities are 0.66 and 0.33.}}}$

Step-by-step explanation:

The number of blue balls = x and number of red balls is half the number of blue balls.

So, the number of red balls is given by

$\dfrac{x}{2}.$

Since the total number of balls in the box is 18, so we must have

$x+\dfrac{x}{2}=18\\\\\Rightarrow \dfrac{3x}{2}=18\\\\\Rightarrow 3x=36\\\\\Rightarrow x=\dfrac{36}{3}\\\\\Rightarrow x=12.$

So, number of blue balls is 12 and the number of red balls is $\dfrac{12}{2}=6.$

Therefore, the probability that a ball drawn at random is blue is

$p_b=\dfrac{\textup{no. of blue balls}}{\textup{total no. of balls}}=\dfrac{12}{18}=0.66$

and the probability that a ball drawn at random is red is

$p_r=\dfrac{\textup{no. of red balls}}{\textup{total number of balls}}=\dfrac{6}{18}=.33.$

Thus, the required probabilities are 0.66 and 0.33.