# 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.

Last updated date: 14th Mar 2023

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Hint: - Here Blue ball’s quantity is unknown But a relation is given between the probability of drawing a blue ball and red ball. so,we use this condition to solve. Probability is the ratio of favorable number of outcomes to the total number of outcomes.

Let the number of blue balls be equal to $x$.

Given data:

Red balls ${\text{ = 5}}$

And according to question

Probability of drawing blue ball ${\text{ = 2}} \times $probability of drawing red ball……… (1)

Now as we know that, Probability ${\text{ = }}\dfrac{{{\text{favorable number of outcomes}}}}{{{\text{Total number of outcomes}}}}$

Total balls ${\text{ = }}x + 5$

Probability of drawing blue ball ${\text{ = }}\dfrac{{{\text{favorable balls}}}}{{{\text{Total balls}}}} = \dfrac{{{\text{Blue balls}}}}{{{\text{Total balls}}}} = \dfrac{x}{{x + 5}}$

Therefore Probability of drawing red ball${\text{ = }}\dfrac{{{\text{favorable balls}}}}{{{\text{Total balls}}}} = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}} = \dfrac{5}{{x + 5}}$

From equation (1)

Probability of drawing blue ball ${\text{ = 2}} \times $probability of drawing red ball

\[

\Rightarrow \dfrac{x}{{x + 5}} = 2 \times \dfrac{5}{{x + 5}} \\

\Rightarrow x = 10 \\

\]

So, the number of blue balls in the bag is equal to 10.

Note: - In such types of questions always remember the formula of probability which is stated above, then calculate the probability of drawing red ball and blue

Let the number of blue balls be equal to $x$.

Given data:

Red balls ${\text{ = 5}}$

And according to question

Probability of drawing blue ball ${\text{ = 2}} \times $probability of drawing red ball……… (1)

Now as we know that, Probability ${\text{ = }}\dfrac{{{\text{favorable number of outcomes}}}}{{{\text{Total number of outcomes}}}}$

Total balls ${\text{ = }}x + 5$

Probability of drawing blue ball ${\text{ = }}\dfrac{{{\text{favorable balls}}}}{{{\text{Total balls}}}} = \dfrac{{{\text{Blue balls}}}}{{{\text{Total balls}}}} = \dfrac{x}{{x + 5}}$

Therefore Probability of drawing red ball${\text{ = }}\dfrac{{{\text{favorable balls}}}}{{{\text{Total balls}}}} = \dfrac{{{\text{Red balls}}}}{{{\text{Total balls}}}} = \dfrac{5}{{x + 5}}$

From equation (1)

Probability of drawing blue ball ${\text{ = 2}} \times $probability of drawing red ball

\[

\Rightarrow \dfrac{x}{{x + 5}} = 2 \times \dfrac{5}{{x + 5}} \\

\Rightarrow x = 10 \\

\]

So, the number of blue balls in the bag is equal to 10.

Note: - In such types of questions always remember the formula of probability which is stated above, then calculate the probability of drawing red ball and blue

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