A bag contains 5 red balls and 'n' green balls. If the P(green ball) = 3 X P(red ball), then what is the value of n?

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Please find below the solution to the asked query:

Given : A bag contains 5 red balls and ' n ' green balls.

We know Probability P ( E ) = $\frac{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{desired} \mathrm{events} \mathrm{n} ( \mathrm{E}\hspace{0.17em})}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{events} \mathrm{n} ( \mathrm{S}\hspace{0.17em})}$

So,
Total number of events n ( S ) = Total number of balls  =  5 + n 

Then

Probability of getting a red ball =  P ( Red ball ) = $\frac{5}{5 +\hspace{0.17em}n}$

And

Probability of getting a green ball =  P ( Green ball ) = $\frac{n}{5 +\hspace{0.17em}n}$

Given  : P ( Green ball ) =  3 $\times$ P ( Red ball )

$\frac{n}{5 +\hspace{0.17em}n}$ = 3 $\times$ $\frac{5}{5 +\hspace{0.17em}n}$

n  =  15                                                                                  ( Ans )

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