A bag contains 6 red balls and some blue balls.

Question:

A bag contains 6 red balls and some blue balls. if the probability of a drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

Solution:

GIVEN: A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball,

TO FIND: the number of blue balls in the bag.

Let the probability of getting a red ball be 

The probability of not getting a red ball or getting a blue ball be 

We know that sum of probability of occurrence of an event and probability of non occurrence of an event is 1.So

$P(E)+P(\bar{E})=1$

$x+2 x=1$

$3 x=1$

$x=\frac{1}{3}$

Hence the probability of getting a red ball is $\frac{1}{3}$

We know that PROBABILITY $=\frac{\text { Number of favourable event }}{\text { Total number of event }}$

$\frac{1}{3}=\frac{6}{\text { Total number of balls }}$

$\Rightarrow$ Total number of balls $=18$ balls

Hence total number of blue balls = total number of balls −red balls

$=18-6$

$=12$ balls

Hence total number of blue balls is 12 balls

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