1 Answer

Eric Andres · Answer 1 · 2021-06-22T14:06:50+0000

Answer:28 green and 35 red

Explanation:

Given

If there are r red counter and g green counter then

Probability of drawing a green counter is
P(g)=(4)/(9)

and
$P(g)=\frac{\text{No of g counter}}{\text{Total no of counter}}$

Thus
$\frac{\text{No of g counter}}{\text{Total no of counter}}=(4)/(9)$

(g)/(g+r)=(4)/(9)

$\Rightarrow 9g=4g+4r$

$\Rightarrow 5g=4r\quad \ldots(i)$

Also if 4 red and 2 green counter is added the probability of drawing a green counter is

$P(g)=(10)/(23)=\frac{\text{No of g counter}}{\text{Total no of counter}}$

$\Rightarrow (10)/(23)=(g+2)/(g+2+r+4)$

$\Rightarrow (10)/(23)=(g+2)/(g+r+6)$

$\Rightarrow 10g+10r+60=23g+46$

$\Rightarrow 10r+14=13g\ quad \ldots(ii)$

Substitute the value of g in equation (ii)[/tex]

$\Rightarrow 10* (5)/(4)g+14=13g$

$\Rightarrow (25)/(2)g+14=13g$

$\Rightarrow g=28$

Therefore
r=35

Thus there 28 green counter and 35 red counter

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