Question

A bag contains red, blue and green balls. The probability of picking a red ball is 1/4, that of picking a green ball is 1/5. if there are 27 blue balls in the bag, find the number of red balls in the bag.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• Total number of balls in bag = 'x'

• Number of red balls be 'r'.

• Number of blue balls be 'b'

• Number of green balls be 'g'

Given that,

$\rm :\longmapsto\:Probability_{ \red{(getting \: red)}} = \dfrac{1}{4}$

$\rm :\longmapsto\:Probability_{ \green{(getting \: green)}} = \dfrac{1}{5}$

$\rm :\implies\:Probability_{\blue{(getting\:blue)}}=1- (P_{\red{(getting\:red)}}+P_{\green{(getting\:green)}}$

$\rm :\longmapsto\:Probability_{ \blue{(getting \: blue)}} = 1 - \dfrac{1}{4} - \dfrac{1}{5}$

$\rm :\longmapsto\:Probability_{ \blue{(getting \: blue)}} = \dfrac{20 - 4 - 5}{20}$

$\rm :\longmapsto\:Probability_{ \blue{(getting \: blue)}} = \dfrac{20 - 9}{20}$

$\rm :\longmapsto\:Probability_{ \blue{(getting \: blue)}} = \dfrac{11}{20}$

Also,

Given that,

Total number of blue balls = 27

We know that,

$\sf \:Probability \: of \: an \: event =\dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$

Thus,

$\rm :\longmapsto\:\dfrac{11}{20} = \dfrac{27}{x}$

$\bf\implies \:x = \dfrac{27 \times 20}{9} = 60$

So

• Total number of balls in bag = 60

Now,

We have

• Total number of balls = 60

• Number of red balls = r

$\rm :\longmapsto\:Probability_{\red{(getting \: red)}} = \dfrac{1}{4}$

$\rm :\longmapsto\:\dfrac{r}{60} = \dfrac{1}{4}$

$\bf\implies \:r \: = \: 15$

$\boxed{ \bf \: Hence \: number \: of \: red \: balls = 15}$

Additional Information :-

Explore more :-

1. The sample space is the collection of all possible outcomes associated with the random experiment.

2. An event associated with a random experiment is a part of the sample space otherwise the probability of an event is 0.

3. The probability of any outcome is a number between 0 and 1 including 0 and 1. That means probability can never be more than 1 and less than 0.

4. The probability of sure event is 1.

5. The probability of impossible event is 0.

6. The sum of the probabilities of all the outcomes associated with a random experiment is 1.